Rework 2D stabilizator

See this page for motivation and description of concepts:
https://github.com/Ichthyostega/blender/wiki

See this video for UI explanation and demonstration of usage
http://vimeo.com/blenderHack/stabilizerdemo

This proposal attempts to improve usability of Blender's image stabilization
feature for real-world footage esp. with moving and panning camera. It builds
upon the feature tracking to get a measurement of 2D image movement.

  - Use a weighted average of movement contributions (instead of a median).
  - Allow for rotation compensation and zoom (image scale) compensation.
  - Allow to pick a different set of tracks for translation and for
    rotation/zoom.
  - Treat translation / rotation / zoom contributions systematically in a
    similar way.
  - Improve handling of partial tracking data with gaps and varying
    start / end points.
  - Have a user definable anchor frame and interpolate / extrapolate data to
    avoid jumping back to "neutral" position when no tracking data is available.
  - Support for travelling and panning shots by including an //intended//
    position/rotation/zoom ("target position"). The idea is for these parameters
    to be //animated// by the user, in order to supply an smooth, intended
    camera movement. This way, we can keep the image content roughly in frame
    even when moving completely away from the initial view.

A known shortcoming is that the pivot point for rotation compensation is set to
the translation compensated image center. This can produce spurious rotation on
travelling shots, which needs to be compensated manually (by animating the
target rotation parameter). There are several possible ways to address that
problem, yet all of them are considered beyond the scope of this improvement
proposal for now.

Own modifications:

- Restrict line length, it's really handy for split-view editing
- In motion tracking we prefer fully human-readable comments, meaning we
  don't use doxygen with it's weird markup and comments are supposed to
  start with capital and end with a full stop,
- Add explicit comparison of pointer to NULL.

Reviewers: sergey

Subscribers: kusi, kdawg, forest-house, mardy, Samoth, plasmasolutions, willolis, sebastian_k, hype, enetheru, sunboy, jta, leon_cheung

Maniphest Tasks: T49036

Differential Revision: https://developer.blender.org/D583

1 files changed, 1239 insertions, 208 deletions

diff --git a/source/blender/blenkernel/intern/tracking_stabilize.c b/source/blender/blenkernel/intern/tracking_stabilize.c
index eb224020977..5642ee83fde 100644
--- a/source/blender/blenkernel/intern/tracking_stabilize.c
+++ b/source/blender/blenkernel/intern/tracking_stabilize.c
@@ -21,6 +21,7 @@
  * Contributor(s): Blender Foundation,
  *                 Sergey Sharybin
  *                 Keir Mierle
+ *                 Ichthyostega
  *
  * ***** END GPL LICENSE BLOCK *****
  */
@@ -28,292 +29,1305 @@
 /** \file blender/blenkernel/intern/tracking_stabilize.c
  *  \ingroup bke
  *
- * This file contains implementation of 2D frame stabilization.
+ * This file contains implementation of 2D image stabilization.
  */
 
 #include <limits.h>
 
 #include "DNA_movieclip_types.h"
+#include "DNA_scene_types.h"
+#include "DNA_anim_types.h"
+#include "RNA_access.h"
 
 #include "BLI_utildefines.h"
+#include "BLI_sort_utils.h"
+#include "BLI_math_vector.h"
 #include "BLI_math.h"
 
 #include "BKE_tracking.h"
+#include "BKE_movieclip.h"
+#include "BKE_fcurve.h"
+#include "BLI_ghash.h"
 
+#include "MEM_guardedalloc.h"
 #include "IMB_imbuf_types.h"
 #include "IMB_imbuf.h"
 
-/* Calculate median point of markers of tracks marked as used for
- * 2D stabilization.
- *
- * NOTE: frame number should be in clip space, not scene space
+
+/* == Parameterization constants == */
+
+/* When measuring the scale changes relative to the rotation pivot point, it
+ * might happen accidentally that a probe point (tracking point), which doesn't
+ * actually move on a circular path, gets very close to the pivot point, causing
+ * the measured scale contribution to go toward infinity. We damp this undesired
+ * effect by adding a bias (floor) to the measured distances, which will
+ * dominate very small distances and thus cause the corresponding track's
+ * contribution to diminish.
+ * Measurements happen in normalized (0...1) coordinates within a frame.
+ */
+static float SCALE_ERROR_LIMIT_BIAS = 0.01f;
+
+/* When to consider a track as completely faded out.
+ * This is used in conjunction with the "disabled" flag of the track
+ * to determine start positions, end positions and gaps
  */
-static bool stabilization_median_point_get(MovieTracking *tracking, int framenr, float median[2])
+static float EPSILON_WEIGHT = 0.005f;
+
+
+
+/* == private working data == */
+
+/* Per track baseline for stabilization, defined at reference frame.
+ * A track's reference frame is chosen as close as possible to the (global)
+ * anchor_frame. Baseline holds the constant part of each track's contribution
+ * to the observed movement; it is calculated at initialization pass, using the
+ * measurement value at reference frame plus the average contribution to fill
+ * the gap between global anchor_frame and the reference frame for this track.
+ * This struct with private working data is associated to the local call context
+ * via `StabContext::private_track_data`
+ */
+typedef struct TrackStabilizationBase {
+	float stabilization_offset_base[2];
+
+	/* measured relative to translated pivot */
+	float stabilization_rotation_base[2][2];
+
+	/* measured relative to translated pivot */
+	float stabilization_scale_base;
+
+	bool is_init_for_stabilization;
+	FCurve *track_weight_curve;
+} TrackStabilizationBase;
+
+/* Tracks are reordered for initialization, starting as close as possible to
+ * anchor_frame
+ */
+typedef struct TrackInitOrder {
+	int sort_value;
+	int reference_frame;
+	MovieTrackingTrack *data;
+} TrackInitOrder;
+
+/* Per frame private working data, for accessing possibly animated values. */
+typedef struct StabContext {
+	MovieClip *clip;
+	MovieTracking *tracking;
+	MovieTrackingStabilization *stab;
+	GHash *private_track_data;
+	FCurve *locinf;
+	FCurve *rotinf;
+	FCurve *scaleinf;
+	FCurve *target_pos[2];
+	FCurve *target_rot;
+	FCurve *target_scale;
+	bool use_animation;
+} StabContext;
+
+
+static TrackStabilizationBase *access_stabilization_baseline_data(
+        StabContext *ctx,
+        MovieTrackingTrack *track)
 {
-	bool ok = false;
-	float min[2], max[2];
-	MovieTrackingTrack *track;
+	return BLI_ghash_lookup(ctx->private_track_data, track);
+}
 
-	INIT_MINMAX2(min, max);
+static void attach_stabilization_baseline_data(
+        StabContext *ctx,
+        MovieTrackingTrack *track,
+        TrackStabilizationBase *private_data)
+{
+	return BLI_ghash_insert(ctx->private_track_data, track, private_data);
+}
 
-	track = tracking->tracks.first;
-	while (track) {
-		if (track->flag & TRACK_USE_2D_STAB) {
-			MovieTrackingMarker *marker = BKE_tracking_marker_get(track, framenr);
+static void discard_stabilization_baseline_data(void *val)
+{
+	if (val != NULL) {
+		MEM_freeN(val);
+	}
+}
 
-			minmax_v2v2_v2(min, max, marker->pos);
 
-			ok = true;
-		}
+/* == access animated values for given frame == */
+
+static FCurve *retrieve_stab_animation(MovieClip *clip,
+                                       const char *data_path,
+                                       int idx)
+{
+	return id_data_find_fcurve(&clip->id,
+	                           &clip->tracking.stabilization,
+	                           &RNA_MovieTrackingStabilization,
+	                           data_path,
+	                           idx,
+	                           NULL);
+}
+
+static FCurve *retrieve_track_weight_animation(MovieClip *clip,
+                                               MovieTrackingTrack *track)
+{
+	return id_data_find_fcurve(&clip->id,
+	                           track,
+	                           &RNA_MovieTrackingTrack,
+	                           "weight_stab",
+	                           0,
+	                           NULL);
+}
 
-		track = track->next;
+static float fetch_from_fcurve(FCurve *animationCurve,
+                               int framenr,
+                               StabContext *ctx,
+                               float default_value)
+{
+	if (ctx && ctx->use_animation && animationCurve) {
+		int scene_framenr = BKE_movieclip_remap_clip_to_scene_frame(ctx->clip,
+		                                                            framenr);
+		return evaluate_fcurve(animationCurve, scene_framenr);
 	}
+	return default_value;
+}
 
-	median[0] = (max[0] + min[0]) / 2.0f;
-	median[1] = (max[1] + min[1]) / 2.0f;
 
-	return ok;
+static float get_animated_locinf(StabContext *ctx, int framenr)
+{
+	return fetch_from_fcurve(ctx->locinf, framenr, ctx, ctx->stab->locinf);
 }
 
-/* Calculate stabilization data (translation, scale and rotation) from
- * given median of first and current frame medians, tracking data and
- * frame number.
- *
- * NOTE: frame number should be in clip space, not scene space
+static float get_animated_rotinf(StabContext *ctx, int framenr)
+{
+	return fetch_from_fcurve(ctx->rotinf, framenr, ctx, ctx->stab->rotinf);
+}
+
+static float get_animated_scaleinf(StabContext *ctx, int framenr)
+{
+	return fetch_from_fcurve(ctx->scaleinf, framenr, ctx, ctx->stab->scaleinf);
+}
+
+static void get_animated_target_pos(StabContext *ctx,
+                                    int framenr,
+		                            float target_pos[2])
+{
+	target_pos[0] = fetch_from_fcurve(ctx->target_pos[0],
+	                                  framenr,
+	                                  ctx,
+	                                  ctx->stab->target_pos[0]);
+	target_pos[1] = fetch_from_fcurve(ctx->target_pos[1],
+	                                  framenr,
+	                                  ctx,
+	                                  ctx->stab->target_pos[1]);
+}
+
+static float get_animated_target_rot(StabContext *ctx, int framenr)
+{
+	return fetch_from_fcurve(ctx->target_rot,
+	                         framenr,
+	                         ctx,
+	                         ctx->stab->target_rot);
+}
+
+static float get_animated_target_scale(StabContext *ctx, int framenr)
+{
+	return fetch_from_fcurve(ctx->target_scale, framenr, ctx, ctx->stab->scale);
+}
+
+static float get_animated_weight(StabContext *ctx,
+                                 MovieTrackingTrack *track,
+                                 int framenr)
+{
+	TrackStabilizationBase *working_data =
+	        access_stabilization_baseline_data(ctx, track);
+	if (working_data && working_data->track_weight_curve) {
+		int scene_framenr = BKE_movieclip_remap_clip_to_scene_frame(ctx->clip,
+		                                                            framenr);
+		return evaluate_fcurve(working_data->track_weight_curve, scene_framenr);
+	}
+	/* Use weight at global 'current frame' as fallback default. */
+	return track->weight_stab;
+}
+
+static void use_values_from_fcurves(StabContext *ctx, bool toggle)
+{
+	if (ctx != NULL) {
+		ctx->use_animation = toggle;
+	}
+}
+
+
+/* Prepare per call private working area.
+ * Used for access to possibly animated values: retrieve available F-curves.
  */
-static void stabilization_calculate_data(MovieTracking *tracking, int framenr, int width, int height,
-                                         const float firstmedian[2], const float median[2],
-                                         float translation[2], float *scale, float *angle)
+static StabContext *initialize_stabilization_working_context(MovieClip *clip)
 {
-	MovieTrackingStabilization *stab = &tracking->stabilization;
+	StabContext *ctx = MEM_callocN(sizeof(StabContext),
+	                               "2D stabilization animation runtime data");
+	ctx->clip = clip;
+	ctx->tracking = &clip->tracking;
+	ctx->stab = &clip->tracking.stabilization;
+	ctx->private_track_data = BLI_ghash_ptr_new(
+	         "2D stabilization per track private working data");
+	ctx->locinf        = retrieve_stab_animation(clip, "influence_location", 0);
+	ctx->rotinf        = retrieve_stab_animation(clip, "influence_rotation", 0);
+	ctx->scaleinf      = retrieve_stab_animation(clip, "influence_scale", 0);
+	ctx->target_pos[0] = retrieve_stab_animation(clip, "target_pos", 0);
+	ctx->target_pos[1] = retrieve_stab_animation(clip, "target_pos", 1);
+	ctx->target_rot    = retrieve_stab_animation(clip, "target_rot", 0);
+	ctx->target_scale  = retrieve_stab_animation(clip, "target_zoom", 0);
+	ctx->use_animation = true;
+	return ctx;
+}
 
-	*scale = (stab->scale - 1.0f) * stab->scaleinf + 1.0f;
-	*angle = 0.0f;
+/* Discard all private working data attached to this call context.
+ * NOTE: We allocate the record for the per track baseline contribution
+ *       locally for each call context (i.e. call to
+ *       BKE_tracking_stabilization_data_get()
+ *       Thus it is correct to discard all allocations found within the
+ *       corresponding _local_ GHash
+ */
+static void discard_stabilization_working_context(StabContext *ctx)
+{
+	if (ctx != NULL) {
+		BLI_ghash_free(ctx->private_track_data,
+		               NULL,
+		               discard_stabilization_baseline_data);
+		MEM_freeN(ctx);
+	}
+}
 
-	translation[0] = (firstmedian[0] - median[0]) * width * (*scale);
-	translation[1] = (firstmedian[1] - median[1]) * height * (*scale);
+static bool is_init_for_stabilization(StabContext *ctx,
+                                      MovieTrackingTrack *track)
+{
+	TrackStabilizationBase *working_data =
+	        access_stabilization_baseline_data(ctx, track);
+	return (working_data != NULL && working_data->is_init_for_stabilization);
+}
+
+static bool is_usable_for_stabilization(StabContext *ctx,
+                                        MovieTrackingTrack *track)
+{
+	return (track->flag & TRACK_USE_2D_STAB) &&
+	       is_init_for_stabilization(ctx, track);
+}
 
-	mul_v2_fl(translation, stab->locinf);
+static bool is_effectively_disabled(StabContext *ctx,
+                                    MovieTrackingTrack *track,
+                                    MovieTrackingMarker *marker)
+{
+	return (marker->flag & MARKER_DISABLED) ||
+	       (EPSILON_WEIGHT > get_animated_weight(ctx, track, marker->framenr));
+}
 
-	if ((stab->flag & TRACKING_STABILIZE_ROTATION) && stab->rot_track && stab->rotinf) {
-		MovieTrackingMarker *marker;
-		float a[2], b[2];
-		float x0 = (float)width / 2.0f, y0 = (float)height / 2.0f;
-		float x = median[0] * width, y = median[1] * height;
 
-		marker = BKE_tracking_marker_get(stab->rot_track, 1);
-		sub_v2_v2v2(a, marker->pos, firstmedian);
-		a[0] *= width;
-		a[1] *= height;
+static int search_closest_marker_index(MovieTrackingTrack *track,
+                                       int ref_frame)
+{
+	MovieTrackingMarker *markers = track->markers;
+	int end = track->markersnr;
+	int i = track->last_marker;
+
+	i = MAX2(0, i);
+	i = MIN2(i, end - 1);
+	for ( ; i < end - 1 && markers[i].framenr <= ref_frame; ++i);
+	for ( ; 0 < i && markers[i].framenr > ref_frame; --i);
+
+	track->last_marker = i;
+	return i;
+}
+
+static void retrieve_next_higher_usable_frame(StabContext *ctx,
+                                              MovieTrackingTrack *track,
+                                              int i,
+                                              int ref_frame,
+                                              int *next_higher)
+{
+	MovieTrackingMarker *markers = track->markers;
+	int end = track->markersnr;
+	BLI_assert(0 <= i && i < end);
+
+	while (i < end &&
+	       (markers[i].framenr < ref_frame ||
+	        is_effectively_disabled(ctx, track, &markers[i])))
+	{
+		++i;
+	}
+	if (i < end && markers[i].framenr < *next_higher) {
+		BLI_assert(markers[i].framenr >= ref_frame);
+		*next_higher = markers[i].framenr;
+	}
+}
+
+static void retrieve_next_lower_usable_frame(StabContext *ctx,
+                                             MovieTrackingTrack *track,
+                                             int i,
+                                             int ref_frame,
+                                             int *next_lower)
+{
+	MovieTrackingMarker *markers = track->markers;
+	BLI_assert(0 <= i && i < end);
+	while (i >= 0 &&
+	       (markers[i].framenr > ref_frame ||
+	        is_effectively_disabled(ctx, track, &markers[i])))
+	{
+		--i;
+	}
+	if (0 <= i && markers[i].framenr > *next_lower) {
+		BLI_assert(markers[i].framenr <= ref_frame);
+		*next_lower = markers[i].framenr;
+	}
+}
+
+/* Find closest frames with usable stabilization data.
+ * A frame counts as _usable_ when there is at least one track marked for
+ * translation stabilization, which has an enabled tracking marker at this very
+ * frame. We search both for the next lower and next higher position, to allow
+ * the caller to interpolate gaps and to extrapolate at the ends of the
+ * definition range.
+ *
+ * NOTE: Regarding performance note that the individual tracks will cache the
+ *       last search position.
+ */
+static void find_next_working_frames(StabContext *ctx,
+                                     int framenr,
+                                     int *next_lower,
+                                     int *next_higher)
+{
+	for (MovieTrackingTrack *track = ctx->tracking->tracks.first;
+	     track != NULL;
+	     track = track->next)
+	{
+		if (is_usable_for_stabilization(ctx, track)) {
+			int startpoint = search_closest_marker_index(track, framenr);
+			retrieve_next_higher_usable_frame(ctx,
+			                                  track,
+			                                  startpoint,
+			                                  framenr,
+			                                  next_higher);
+			retrieve_next_lower_usable_frame(ctx,
+			                                 track,
+			                                 startpoint,
+			                                 framenr,
+			                                 next_lower);
+		}
+	}
+}
+
 
-		marker = BKE_tracking_marker_get(stab->rot_track, framenr);
-		sub_v2_v2v2(b, marker->pos, median);
-		b[0] *= width;
-		b[1] *= height;
+/* Find active (enabled) marker closest to the reference frame. */
+static MovieTrackingMarker *get_closest_marker(StabContext *ctx,
+                                               MovieTrackingTrack *track,
+                                               int ref_frame)
+{
+	if (track->markersnr > 0) {
+		int next_lower = MINAFRAME;
+		int next_higher = MAXFRAME;
+		int  i = search_closest_marker_index(track, ref_frame);
+		retrieve_next_higher_usable_frame(ctx, track, i, ref_frame, &next_higher);
+		retrieve_next_lower_usable_frame(ctx, track, i, ref_frame, &next_lower);
+
+		if ((next_higher - ref_frame) < (ref_frame - next_lower)) {
+			return BKE_tracking_marker_get_exact(track, next_higher);
+		}
+		else {
+			return BKE_tracking_marker_get_exact(track, next_lower);
+		}
+	}
+	return NULL;
+}
 
-		*angle = -atan2f(a[0] * b[1] - a[1] * b[0], a[0] * b[0] + a[1] * b[1]);
-		*angle *= stab->rotinf;
 
-		/* convert to rotation around image center */
-		translation[0] -= (x0 + (x - x0) * cosf(*angle) - (y - y0) * sinf(*angle) - x) * (*scale);
-		translation[1] -= (y0 + (x - x0) * sinf(*angle) + (y - y0) * cosf(*angle) - y) * (*scale);
+/* Retrieve tracking data, if available and applicable for this frame.
+ * The returned weight value signals the validity; data recorded for this
+ * tracking marker on the exact requested frame is output with the full weight
+ * of this track, while gaps in the data sequence cause the weight to go to zero.
+ */
+static MovieTrackingMarker *get_tracking_data_point(
+        StabContext *ctx,
+        MovieTrackingTrack *track,
+        int framenr,
+        float *weight)
+{
+	MovieTrackingMarker *marker = BKE_tracking_marker_get(track, framenr);
+	if (marker && marker->framenr == framenr && !(marker->flag & MARKER_DISABLED)) {
+		*weight = get_animated_weight(ctx, track, framenr);
+		return marker;
+	}
+	else {
+		/* no marker at this frame (=gap) or marker disabled */
+		*weight = 0.0f;
+		return NULL;
 	}
 }
 
-/* Calculate factor of a scale, which will eliminate black areas
- * appearing on the frame caused by frame translation.
+/* Calculate the contribution of a single track at the time position (frame) of
+ * the given marker. Each track has a local reference frame, which is as close
+ * as possible to the global anchor_frame. Thus the translation contribution is
+ * comprised of the offset relative to the image position at that reference
+ * frame, plus a guess of the contribution for the time span between the
+ * anchor_frame and the local reference frame of this track. The constant part
+ * of this contribution is precomputed initially. At the anchor_frame, by
+ * definition the contribution of all tracks is zero, keeping the frame in place.
+ *
+ * track_ref is per track baseline contribution at reference frame; filled in at
+ *           initialization
+ * marker is tracking data to use as contribution for current frame.
+ * result_offset is a total cumulated contribution of this track,
+ *               relative to the stabilization anchor_frame,
+ *               in normalized (0...1) coordinates.
+ */
+static void translation_contribution(TrackStabilizationBase *track_ref,
+                                     MovieTrackingMarker *marker,
+                                     float result_offset[2])
+{
+	add_v2_v2v2(result_offset,
+	            track_ref->stabilization_offset_base,
+	            marker->pos);
+}
+
+/* Similar to the ::translation_contribution(), the rotation contribution is
+ * comprised of the contribution by this individual track, and the averaged
+ * contribution from anchor_frame to the ref point of this track.
+ * - Contribution is in terms of angles, -pi < angle < +pi, and all averaging
+ *   happens in this domain.
+ * - Yet the actual measurement happens as vector between pivot and the current
+ *   tracking point
+ * - Currently we use the center of frame as approximation for the rotation pivot
+ *   point.
+ * - Moreover, the pivot point has to be compensated for the already determined
+ *   shift offset, in order to get the pure rotation around the pivot.
+ *   To turn this into a _contribution_, the likewise corrected angle at the
+ *   reference frame has to be subtracted, to get only the pure angle difference
+ *   this tracking point has captured.
+ * - To get from vectors to angles, we have to go through an arcus tangens,
+ *   which involves the issue of the definition range: the resulting angles will
+ *   flip by 360deg when the measured vector passes from the 2nd to the third
+ *   quadrant, thus messing up the average calculation. Since _any_ tracking
+ *   point might be used, these problems are quite common in practice.
+ * - Thus we perform the subtraction of the reference and the addition of the
+ *   baseline contribution in polar coordinates as simple addition of angles;
+ *   since these parts are fixed, we can bake them into a rotation matrix.
+ *   With this approach, the border of the arcus tangens definition range will
+ *   be reached only, when the _whole_ contribution approaches +- 180deg,
+ *   meaning we've already tilted the frame upside down. This situation is way
+ *   less common and can be tolerated.
+ * - As an additional feature, when activated, also changes in image scale
+ *   relative to the rotation center can be picked up. To handle those values
+ *   in the same framework, we average the scales as logarithms.
+ *
+ * aspect is a total aspect ratio of the undistorted image (includes fame and
+ * pixel aspect).
+ */
+static void rotation_contribution(TrackStabilizationBase *track_ref,
+                                  MovieTrackingMarker *marker,
+                                  float aspect,
+                                  float target_pos[2],
+                                  float averaged_translation_contribution[2],
+                                  float *result_angle,
+                                  float *result_scale)
+{
+	float len;
+	float pos[2];
+	float pivot[2];
+	copy_v2_fl(pivot, 0.5f);  /* Use center of frame as hard wired pivot. */
+	add_v2_v2(pivot, averaged_translation_contribution);
+	sub_v2_v2(pivot, target_pos);
+	sub_v2_v2v2(pos, marker->pos, pivot);
+
+	pos[0] *= aspect;
+	mul_m2v2(track_ref->stabilization_rotation_base, pos);
+
+	*result_angle = atan2f(pos[1],pos[0]);
+
+	len = len_v2(pos) + SCALE_ERROR_LIMIT_BIAS;
+	*result_scale = len * track_ref->stabilization_scale_base;
+	BLI_assert(0.0 < *result_scale);
+}
+
+
+/* Weighted average of the per track cumulated contributions at given frame.
+ * Returns truth if all desired calculations could be done and all averages are
+ * available.
+ *
+ * NOTE: Even if the result is not `true`, the returned translation and angle
+ *       are always sensible and as good as can be. Especially in the
+ *       initialization phase we might not be able to get any average (yet) or
+ *       get only a translation value. Since initialization visits tracks in a
+ *       specific order, starting from anchor_frame, the result is logically
+ *       correct non the less. But under normal operation conditions,
+ *       a result of `false` should disable the stabilization function
  */
-static float stabilization_calculate_autoscale_factor(MovieTracking *tracking, int width, int height)
+static bool average_track_contributions(StabContext *ctx,
+                                        int framenr,
+                                        float aspect,
+                                        float r_translation[2],
+                                        float *r_angle,
+                                        float *r_scale_step)
 {
-	float firstmedian[2];
+	bool ok;
+	float weight_sum;
+	MovieTrackingTrack *track;
+	MovieTracking *tracking = ctx->tracking;
 	MovieTrackingStabilization *stab = &tracking->stabilization;
-	float aspect = tracking->camera.pixel_aspect;
-
-	/* Early output if stabilization data is already up-to-date. */
-	if (stab->ok)
-		return stab->scale;
-
-	/* See comment in BKE_tracking_stabilization_data_get about first frame. */
-	if (stabilization_median_point_get(tracking, 1, firstmedian)) {
-		int sfra = INT_MAX, efra = INT_MIN, cfra;
-		float scale = 1.0f;
-		MovieTrackingTrack *track;
-
-		stab->scale = 1.0f;
-
-		/* Calculate frame range of tracks used for stabilization. */
-		track = tracking->tracks.first;
-		while (track) {
-			if (track->flag & TRACK_USE_2D_STAB ||
-			    ((stab->flag & TRACKING_STABILIZE_ROTATION) && track == stab->rot_track))
-			{
-				sfra = min_ii(sfra, track->markers[0].framenr);
-				efra = max_ii(efra, track->markers[track->markersnr - 1].framenr);
-			}
+	BLI_assert(stab->flag & TRACKING_2D_STABILIZATION);
 
-			track = track->next;
+	zero_v2(r_translation);
+	*r_scale_step = 0.0f;  /* logarithm */
+	*r_angle = 0.0f;
+
+	ok = false;
+	weight_sum = 0.0f;
+	for (track = tracking->tracks.first; track; track = track->next) {
+		if (!is_init_for_stabilization(ctx, track)) {
+			continue;
+		}
+		if (track->flag & TRACK_USE_2D_STAB) {
+			float weight = 0.0f;
+			MovieTrackingMarker *marker = get_tracking_data_point(ctx,
+			                                                      track,
+			                                                      framenr,
+			                                                      &weight);
+			if (marker) {
+				TrackStabilizationBase *stabilization_base =
+				       access_stabilization_baseline_data(ctx, track);
+				BLI_assert(stabilization_base != NULL);
+				float offset[2];
+				weight_sum += weight;
+				translation_contribution(stabilization_base, marker, offset);
+				mul_v2_fl(offset, weight);
+				add_v2_v2(r_translation, offset);
+				ok |= (weight_sum > EPSILON_WEIGHT);
+			}
 		}
+	}
+	if (!ok) {
+		return false;
+	}
 
-		/* For every frame we calculate scale factor needed to eliminate black
-		 * area and choose largest scale factor as final one.
-		 */
-		for (cfra = sfra; cfra <= efra; cfra++) {
-			float median[2];
-			float translation[2], angle, tmp_scale;
-			int i;
-			float mat[4][4];
-			float points[4][2] = {{0.0f, 0.0f}, {0.0f, height}, {width, height}, {width, 0.0f}};
-			float si, co;
+	r_translation[0] /= weight_sum;
+	r_translation[1] /= weight_sum;
 
-			stabilization_median_point_get(tracking, cfra, median);
+	if (!(stab->flag & TRACKING_STABILIZE_ROTATION)) {
+		return ok;
+	}
 
-			stabilization_calculate_data(tracking, cfra, width, height, firstmedian, median, translation,
-			                             &tmp_scale, &angle);
+	ok = false;
+	weight_sum = 0.0f;
+	for (track = tracking->tracks.first; track; track = track->next) {
+		if (!is_init_for_stabilization(ctx, track)) {
+			continue;
+		}
+		if (track->flag & TRACK_USE_2D_STAB_ROT) {
+			float weight = 0.0f;
+			MovieTrackingMarker *marker = get_tracking_data_point(ctx,
+			                                                      track,
+			                                                      framenr,
+			                                                      &weight);
+			if (marker) {
+				TrackStabilizationBase *stabilization_base =
+				        access_stabilization_baseline_data(ctx, track);
+				BLI_assert(stabilization_base != NULL);
+				float rotation, scale;
+				float target_pos[2];
+				weight_sum += weight;
+				get_animated_target_pos(ctx, framenr, target_pos);
+				rotation_contribution(stabilization_base,
+				                      marker,
+				                      aspect,
+				                      target_pos,
+				                      r_translation,
+				                      &rotation,
+				                      &scale);
+				*r_angle += rotation * weight;
+				if (stab->flag & TRACKING_STABILIZE_SCALE) {
+					*r_scale_step += logf(scale) * weight;
+				}
+				else {
+					*r_scale_step = 0;
+				}
+				ok |= (weight_sum > EPSILON_WEIGHT);
+			}
+		}
+	}
+	if (ok) {
+		*r_scale_step /= weight_sum;
+		*r_angle /= weight_sum;
+	}
+	else {
+		/* We reach this point because translation could be calculated,
+		 * but rotation/scale found no data to work on.
+		 */
+		*r_scale_step = 0.0f;
+		*r_angle = 0.0f;
+	}
+	return true;
+}
 
-			BKE_tracking_stabilization_data_to_mat4(width, height, aspect, translation, 1.0f, angle, mat);
 
-			si = sinf(angle);
-			co = cosf(angle);
+/* Linear interpolation of data retrieved at two measurement points.
+ * This function is used to fill gaps in the middle of the covered area,
+ * at frames without any usable tracks for stabilization.
+ *
+ * framenr is a position to interpolate for.
+ * frame_a is a valid measurement point below framenr
+ * frame_b is a valid measurement point above framenr
+ * Returns truth if both measurements could actually be retrieved.
+ * Otherwise output parameters remain unaltered
+ */
+static bool interpolate_averaged_track_contributions(StabContext *ctx,
+                                                     int framenr,
+                                                     int frame_a,
+                                                     int frame_b,
+                                                     float aspect,
+                                                     float translation[2],
+                                                     float *r_angle,
+                                                     float *r_scale_step)
+{
+	float t, s;
+	float trans_a[2], trans_b[2];
+	float angle_a, angle_b;
+	float scale_a, scale_b;
+	bool success = false;
+
+	BLI_assert(frame_a <= frame_b);
+	BLI_assert(frame_a <= framenr);
+	BLI_assert(framenr <= frame_b);
+
+	t = ((float)framenr - frame_a) / (frame_b - frame_a);
+	s = 1.0f - t;
+
+	success = average_track_contributions(ctx, frame_a, aspect, trans_a, &angle_a, &scale_a);
+	if (!success) {
+		return false;
+	}
+	success = average_track_contributions(ctx, frame_b, aspect, trans_b, &angle_b, &scale_b);
+	if (!success) {
+		return false;
+	}
 
-			for (i = 0; i < 4; i++) {
-				int j;
-				float a[3] = {0.0f, 0.0f, 0.0f}, b[3] = {0.0f, 0.0f, 0.0f};
+	interp_v2_v2v2(translation, trans_a, trans_b, t);
+	*r_scale_step = s * scale_a + t * scale_b;
+	*r_angle = s * angle_a + t * angle_b;
+	return true;
+}
 
-				copy_v3_v3(a, points[i]);
-				copy_v3_v3(b, points[(i + 1) % 4]);
 
-				mul_m4_v3(mat, a);
-				mul_m4_v3(mat, b);
+/* Reorder tracks starting with those providing a tracking data frame
+ * closest to the global anchor_frame. Tracks with a gap at anchor_frame or
+ * starting farer away from anchor_frame altogether will be visited later.
+ * This allows to build up baseline contributions incrementally.
+ *
+ * order is an array for sorting the tracks. Must be of suitable size to hold
+ * all tracks.
+ * Returns number of actually usable tracks, can be less than the overall number
+ * of tracks.
+ *
+ * NOTE: After returning, the order array holds entries up to the number of
+ *       usable tracks, appropriately sorted starting with the closest tracks.
+ *       Initialization includes disabled tracks, since they might be enabled
+ *       through automation later.
+ */
+static int establish_track_initialization_order(StabContext *ctx,
+                                                TrackInitOrder *order)
+{
+	size_t tracknr = 0;
+	MovieTrackingTrack *track;
+	MovieTracking *tracking = ctx->tracking;
+	int anchor_frame = tracking->stabilization.anchor_frame;
 
-				for (j = 0; j < 4; j++) {
-					float point[3] = {points[j][0], points[j][1], 0.0f};
-					float v1[3], v2[3];
+	for (track = tracking->tracks.first; track != NULL; track = track->next) {
+		MovieTrackingMarker *marker;
+		order[tracknr].data = track;
+		marker = get_closest_marker(ctx, track, anchor_frame);
+		if (marker != NULL &&
+			(track->flag & (TRACK_USE_2D_STAB | TRACK_USE_2D_STAB_ROT)))
+		{
+			order[tracknr].sort_value = abs(marker->framenr - anchor_frame);
+			order[tracknr].reference_frame = marker->framenr;
+			++tracknr;
+		}
+	}
+	if (tracknr) {
+		qsort(order, tracknr, sizeof(TrackInitOrder), BLI_sortutil_cmp_int);
+	}
+	return tracknr;
+}
 
-					sub_v3_v3v3(v1, b, a);
-					sub_v3_v3v3(v2, point, a);
 
-					if (cross_v2v2(v1, v2) >= 0.0f) {
-						const float rotDx[4][2] = {{1.0f, 0.0f}, {0.0f, -1.0f}, {-1.0f, 0.0f}, {0.0f, 1.0f}};
-						const float rotDy[4][2] = {{0.0f, 1.0f}, {1.0f, 0.0f}, {0.0f, -1.0f}, {-1.0f, 0.0f}};
+/* Setup the constant part of this track's contribution to the determined frame
+ * movement. Tracks usually don't provide tracking data for every frame. Thus,
+ * for determining data at a given frame, we split up the contribution into a
+ * part covered by actual measurements on this track, and the initial gap
+ * between this track's reference frame and the global anchor_frame.
+ * The (missing) data for the gap can be substituted by the average offset
+ * observed by the other tracks covering the gap. This approximation doesn't
+ * introduce wrong data, but it records data with incorrect weight. A totally
+ * correct solution would require us to average the contribution per frame, and
+ * then integrate stepwise over all frames -- which of course would be way more
+ * expensive, especially for longer clips. To the contrary, our solution
+ * cumulates the total contribution per track and averages afterwards over all
+ * tracks; it can thus be calculated just based on the data of a single frame,
+ * plus the "baseline" for the reference frame, which is what we are computing
+ * here.
+ *
+ * Since we're averaging _contributions_, we have to calculate the _difference_
+ * of the measured position at current frame and the position at the reference
+ * frame. But the "reference" part of this difference is constant and can thus
+ * be packed together with the baseline contribution into a single precomputed
+ * vector per track.
+ *
+ * In case of the rotation contribution, the principle is the same, but we have
+ * to compensate for the already determined translation and measure the pure
+ * rotation, simply because this is how we model the offset: shift plus rotation
+ * around the shifted rotation center. To circumvent problems with the
+ * definition range of the arcus tangens function, we perform this baseline
+ * addition and reference angle subtraction in polar coordinates and bake this
+ * operation into a precomputed rotation matrix.
+ *
+ * track is a track to be initialized to initialize
+ * reference_frame is a local frame for this track, the closest pick to the
+ *                 global anchor_frame.
+ * aspect is a total aspect ratio of the undistorted image (includes fame and
+ *        pixel aspect).
+ * target_pos is a possibly animated target position as set by the user for
+ *            the reference_frame
+ * average_translation is a value observed by the _other_ tracks for the gap
+ *                     between reference_frame and anchor_frame. This
+ *                     average must not contain contributions of frames
+ *                     not yet initialized
+ * average_angle in a similar way, the rotation value observed by the
+ *               _other_ tracks.
+ * average_scale_step is an image scale factor observed on average by the other
+ *                    tracks for this frame. This value is recorded and
+ *                    averaged as logarithm. The recorded scale changes
+ *                    are damped for very small contributions, to limit
+ *                    the effect of probe points approaching the pivot
+ *                    too closely.
+ *
+ * NOTE: when done, this track is marked as initialized
+ */
+static void initialize_track_for_stabilization(StabContext *ctx,
+                                               MovieTrackingTrack *track,
+                                               int reference_frame,
+                                               float aspect,
+                                               const float target_pos[2],
+                                               const float average_translation[2],
+                                               float average_angle,
+                                               float average_scale_step)
+{
+	float pos[2], angle, len;
+	float pivot[2];
+	TrackStabilizationBase *local_data =
+	        access_stabilization_baseline_data(ctx, track);
+	MovieTrackingMarker *marker =
+	        BKE_tracking_marker_get_exact(track, reference_frame);
+	/* Logic for initialization order ensures there *is* a marker on that
+	 * very frame.
+	 */
+	BLI_assert(marker != NULL);
+	BLI_assert(local_data != NULL);
 
-						float dx = translation[0] * rotDx[j][0] + translation[1] * rotDx[j][1],
-						      dy = translation[0] * rotDy[j][0] + translation[1] * rotDy[j][1];
+	/* Per track baseline value for translation. */
+	sub_v2_v2v2(local_data->stabilization_offset_base,
+	            average_translation,
+	            marker->pos);
 
-						float w, h, E, F, G, H, I, J, K, S;
+	/* Per track baseline value for rotation. */
+	copy_v2_fl(pivot, 0.5f);  /* Use center of frame as hard wired pivot. */
+	add_v2_v2(pivot, average_translation);
+	sub_v2_v2(pivot, target_pos);
+	sub_v2_v2v2(pos, marker->pos, pivot);
 
-						if (j % 2) {
-							w = (float)height / 2.0f;
-							h = (float)width / 2.0f;
-						}
-						else {
-							w = (float)width / 2.0f;
-							h = (float)height / 2.0f;
-						}
+	pos[0] *= aspect;
+	angle = average_angle - atan2f(pos[1],pos[0]);
+	rotate_m2(local_data->stabilization_rotation_base, angle);
 
-						E = -w * co + h * si;
-						F = -h * co - w * si;
+	/* Per track baseline value for zoom. */
+	len = len_v2(pos) + SCALE_ERROR_LIMIT_BIAS;
+	local_data->stabilization_scale_base = expf(average_scale_step) / len;
 
-						if ((i % 2) == (j % 2)) {
-							G = -w * co - h * si;
-							H = h * co - w * si;
-						}
-						else {
-							G = w * co + h * si;
-							H = -h * co + w * si;
-						}
+	local_data->is_init_for_stabilization = true;
+}
 
-						I = F - H;
-						J = G - E;
-						K = G * F - E * H;
 
-						S = (-w * I - h * J) / (dx * I + dy * J + K);
+static void initialize_all_tracks(StabContext *ctx, float aspect)
+{
+	size_t i, track_cnt = 0;
+	MovieClip *clip = ctx->clip;
+	MovieTracking *tracking = ctx->tracking;
+	MovieTrackingTrack *track;
+	TrackInitOrder *order;
 
-						scale = max_ff(scale, S);
-					}
-				}
-			}
+	/* Attempt to start initialization at anchor_frame.
+	 * By definition, offset contribution is zero there.
+	 */
+	int reference_frame = tracking->stabilization.anchor_frame;
+	float average_angle=0, average_scale_step=0;
+	float average_translation[2];
+	float target_pos_at_ref_frame[2];
+	zero_v2(target_pos_at_ref_frame);
+	zero_v2(average_translation);
+
+	/* Initialize private working data. */
+	for (track = tracking->tracks.first; track != NULL; track = track->next) {
+		TrackStabilizationBase *local_data =
+		        access_stabilization_baseline_data(ctx, track);
+		if (!local_data) {
+			local_data = MEM_callocN(sizeof(TrackStabilizationBase),
+			                         "2D stabilization per track baseline data");
+			attach_stabilization_baseline_data(ctx, track, local_data);
 		}
+		BLI_assert(local_data != NULL);
+		local_data->track_weight_curve = retrieve_track_weight_animation(clip,
+		                                                                 track);
+		local_data->is_init_for_stabilization = false;
 
-		stab->scale = scale;
+		++track_cnt;
+	}
+	if (!track_cnt) {
+		return;
+	}
 
-		if (stab->maxscale > 0.0f)
-			stab->scale = min_ff(stab->scale, stab->maxscale);
+	order = MEM_mallocN(track_cnt * sizeof(TrackInitOrder),
+	                    "stabilization track order");
+	if (!order) {
+		return;
 	}
-	else {
-		stab->scale = 1.0f;
+
+	track_cnt = establish_track_initialization_order(ctx, order);
+	if (track_cnt == 0) {
+		goto cleanup;
 	}
 
-	stab->ok = true;
+	for (i = 0; i < track_cnt; ++i) {
+		track = order[i].data;
+		if (reference_frame != order[i].reference_frame) {
+			reference_frame = order[i].reference_frame;
+			average_track_contributions(ctx,
+			                            reference_frame,
+			                            aspect,
+			                            average_translation,
+			                            &average_angle,
+			                            &average_scale_step);
+			get_animated_target_pos(ctx,
+			                        reference_frame,
+			                        target_pos_at_ref_frame);
+		}
+		initialize_track_for_stabilization(ctx,
+		                                   track,
+		                                   reference_frame,
+		                                   aspect,
+		                                   target_pos_at_ref_frame,
+		                                   average_translation,
+		                                   average_angle,
+		                                   average_scale_step);
+	}
 
-	return stab->scale;
+cleanup:
+	MEM_freeN(order);
 }
 
-/* Get stabilization data (translation, scaling and angle) for a given frame.
+
+/* Retrieve the measurement of frame movement by averaging contributions of
+ * active tracks.
  *
- * NOTE: frame number should be in clip space, not scene space
+ * translation is a measurement in normalized 0..1 coordinates.
+ * angle is a measurement in radians -pi..+pi counter clockwise relative to
+ *       translation compensated frame center
+ * scale_step is a measurement of image scale changes, in logarithmic scale
+ *            (zero means scale == 1)
+ * Returns calculation enabled and all data retrieved as expected for this frame.
+ *
+ * NOTE: when returning `false`, output parameters are reset to neutral values.
  */
-void BKE_tracking_stabilization_data_get(MovieTracking *tracking, int framenr, int width, int height,
-                                         float translation[2], float *scale, float *angle)
+static bool stabilization_determine_offset_for_frame(StabContext *ctx,
+                                                     int framenr,
+                                                     float aspect,
+                                                     float r_translation[2],
+                                                     float *r_angle,
+                                                     float *r_scale_step)
 {
-	float firstmedian[2], median[2];
-	MovieTrackingStabilization *stab = &tracking->stabilization;
+	bool success = false;
 
 	/* Early output if stabilization is disabled. */
-	if ((stab->flag & TRACKING_2D_STABILIZATION) == 0) {
-		zero_v2(translation);
-		*scale = 1.0f;
-		*angle = 0.0f;
+	if ((ctx->stab->flag & TRACKING_2D_STABILIZATION) == 0) {
+		zero_v2(r_translation);
+		*r_scale_step = 0.0f;
+		*r_angle = 0.0f;
+		return false;
+	}
 
-		return;
+	success = average_track_contributions(ctx,
+	                                      framenr,
+	                                      aspect,
+	                                      r_translation,
+	                                      r_angle,
+	                                      r_scale_step);
+	if (!success) {
+		/* Try to hold extrapolated settings beyond the definition range
+		 * and to interpolate in gaps without any usable tracking data
+		 * to prevent sudden jump to image zero position.
+		 */
+		int next_lower = MINAFRAME;
+		int next_higher = MAXFRAME;
+		use_values_from_fcurves(ctx, true);
+		find_next_working_frames(ctx, framenr, &next_lower, &next_higher);
+		if (next_lower >= MINFRAME && next_higher < MAXFRAME) {
+			success = interpolate_averaged_track_contributions(ctx,
+			                                                   framenr,
+			                                                   next_lower,
+			                                                   next_higher,
+			                                                   aspect,
+			                                                   r_translation,
+			                                                   r_angle,
+			                                                   r_scale_step);
+		}
+		else if (next_higher < MAXFRAME) {
+			/* Before start of stabilized range: extrapolate start point
+			 * settings.
+			 */
+			success = average_track_contributions(ctx,
+			                                      next_higher,
+			                                      aspect,
+			                                      r_translation,
+			                                      r_angle,
+			                                      r_scale_step);
+		}
+		else if (next_lower >= MINFRAME) {
+			/* After end of stabilized range: extrapolate end point settings. */
+			success = average_track_contributions(ctx,
+			                                      next_lower,
+			                                      aspect,
+			                                      r_translation,
+			                                      r_angle,
+			                                      r_scale_step);
+		}
+		use_values_from_fcurves(ctx, false);
 	}
+	return success;
+}
 
-	/* Even if tracks does not start at frame 1, their position will
-	 * be estimated at this frame, which will give reasonable result
-	 * in most of cases.
-	 *
-	 * However, it's still better to replace this with real first
-	 * frame number at which tracks are appearing.
+/* Calculate stabilization data (translation, scale and rotation) from given raw
+ * measurements. Result is in absolute image dimensions (expanded image, square
+ * pixels), includes automatic or manual scaling and compensates for a target
+ * frame position, if given.
+ *
+ * size is a size of the expanded image, the width in pixels is size * aspect.
+ * aspect is a ratio (width / height) of the effective canvas (square pixels).
+ * do_compensate denotes whether to actually output values necessary to
+ *               _compensate_ the determined frame movement.
+ *               Otherwise, the effective target movement is returned.
+ */
+static void stabilization_calculate_data(StabContext *ctx,
+                                         int framenr,
+                                         int size,
+                                         float aspect,
+                                         bool do_compensate,
+                                         float scale_step,
+                                         float r_translation[2],
+                                         float *r_scale,
+                                         float *r_angle)
+{
+	float target_pos[2];
+	float scaleinf = get_animated_scaleinf(ctx, framenr);
+
+	*r_scale = (get_animated_target_scale(ctx,framenr) - 1.0f) * scaleinf + 1.0f;
+
+	if (ctx->stab->flag & TRACKING_STABILIZE_SCALE) {
+		*r_scale *= expf(scale_step * scaleinf);  /* Averaged in log scale */
+	}
+
+	mul_v2_fl(r_translation, get_animated_locinf(ctx, framenr));
+	*r_angle *= get_animated_rotinf(ctx, framenr);
+
+	/* Compensate for a target frame position.
+	 * This allows to follow tracking / panning shots in a semi manual fashion,
+	 * when animating the settings for the target frame position.
 	 */
-	if (stabilization_median_point_get(tracking, 1, firstmedian)) {
-		stabilization_median_point_get(tracking, framenr, median);
+	get_animated_target_pos(ctx, framenr, target_pos);
+	sub_v2_v2(r_translation, target_pos);
+	*r_angle -= get_animated_target_rot(ctx,framenr);
 
-		if ((stab->flag & TRACKING_AUTOSCALE) == 0)
-			stab->scale = 1.0f;
+	/* Convert from relative to absolute coordinates, square pixels. */
+	r_translation[0] *= (float)size * aspect;
+	r_translation[1] *= (float)size;
+
+	/* Output measured data, or inverse of the measured values for
+	 * compensation?
+	 */
+	if (do_compensate) {
+		mul_v2_fl(r_translation, -1.0f);
+		*r_angle *= -1.0f;
+		if (*r_scale != 0.0f) {
+			*r_scale = 1.0f / *r_scale;
+		}
+	}
+}
 
-		if (!stab->ok) {
-			if (stab->flag & TRACKING_AUTOSCALE)
-				stabilization_calculate_autoscale_factor(tracking, width, height);
 
-			stabilization_calculate_data(tracking, framenr, width, height, firstmedian, median,
-			                             translation, scale, angle);
+/* Determine the inner part of the frame, which is always safe to use.
+ * When enlarging the image by the inverse of this factor, any black areas
+ * appearing due to frame translation and rotation will be removed.
+ *
+ * NOTE: When calling this function, basic initialization of tracks must be
+ *       done already
+ */
+static void stabilization_determine_safe_image_area(StabContext *ctx,
+                                                    int size,
+                                                    float image_aspect)
+{
+	MovieTrackingStabilization *stab = ctx->stab;
+	float pixel_aspect = ctx->tracking->camera.pixel_aspect;
 
-			stab->ok = true;
+	int sfra = INT_MAX, efra = INT_MIN, cfra;
+	float scale = 1.0f, scale_step = 0.0f;
+	MovieTrackingTrack *track;
+	stab->scale = 1.0f;
+
+	/* Calculate maximal frame range of tracks where stabilization is active. */
+	for (track = ctx->tracking->tracks.first; track; track = track->next) {
+		if ((track->flag & TRACK_USE_2D_STAB) ||
+			((stab->flag & TRACKING_STABILIZE_ROTATION) &&
+			 (track->flag & TRACK_USE_2D_STAB_ROT)))
+		{
+			int first_frame = track->markers[0].framenr;
+			int last_frame  = track->markers[track->markersnr - 1].framenr;
+			sfra = min_ii(sfra, first_frame);
+			efra = max_ii(efra, last_frame);
 		}
-		else {
-			stabilization_calculate_data(tracking, framenr, width, height, firstmedian, median,
-			                             translation, scale, angle);
+	}
+
+	/* For every frame we calculate scale factor needed to eliminate black border area
+	 * and choose largest scale factor as final one.
+	 */
+	for (cfra = sfra; cfra <= efra; cfra++) {
+		float translation[2], angle, tmp_scale;
+		int i;
+		float mat[4][4];
+		float points[4][2] = {{0.0f, 0.0f},
+		                      {0.0f, size},
+		                      {image_aspect * size, size},
+		                      {image_aspect * size, 0.0f}};
+		float si, co;
+		bool do_compensate = true;
+
+		stabilization_determine_offset_for_frame(ctx,
+		                                         cfra,
+		                                         image_aspect,
+		                                         translation,
+		                                         &angle,
+		                                         &scale_step);
+		stabilization_calculate_data(ctx,
+		                             cfra,
+		                             size,
+		                             image_aspect,
+		                             do_compensate,
+		                             scale_step,
+		                             translation,
+		                             &tmp_scale,
+		                             &angle);
+
+		BKE_tracking_stabilization_data_to_mat4(size * image_aspect,
+		                                        size,
+		                                        pixel_aspect,
+		                                        translation,
+		                                        1.0f,
+		                                        angle,
+		                                        mat);
+
+		si = sinf(angle);
+		co = cosf(angle);
+
+		/* Investigate the transformed border lines for this frame;
+		 * find out, where it cuts the original frame.
+		 */
+		for (i = 0; i < 4; i++) {
+			int j;
+			float a[3] = {0.0f, 0.0f, 0.0f},
+			      b[3] = {0.0f, 0.0f, 0.0f};
+
+			copy_v2_v2(a, points[i]);
+			copy_v2_v2(b, points[(i + 1) % 4]);
+			a[2] = b[2] = 0.0f;
+
+			mul_m4_v3(mat, a);
+			mul_m4_v3(mat, b);
+
+			for (j = 0; j < 4; j++) {
+				float point[3] = {points[j][0], points[j][1], 0.0f};
+				float v1[3], v2[3];
+
+				sub_v3_v3v3(v1, b, a);
+				sub_v3_v3v3(v2, point, a);
+
+				if (cross_v2v2(v1, v2) >= 0.0f) {
+					const float rot_dx[4][2] = {{1.0f, 0.0f},
+					                            {0.0f, -1.0f},
+					                            {-1.0f, 0.0f},
+					                            {0.0f, 1.0f}};
+					const float rot_dy[4][2] = {{0.0f, 1.0f},
+					                            {1.0f, 0.0f},
+					                            {0.0f, -1.0f},
+					                            {-1.0f, 0.0f}};
+
+					float dx = translation[0] * rot_dx[j][0] +
+					           translation[1] * rot_dx[j][1],
+					      dy = translation[0] * rot_dy[j][0] +
+					           translation[1] * rot_dy[j][1];
+
+					float w, h, E, F, G, H, I, J, K, S;
+
+					if (j % 2) {
+						w = (float)size / 2.0f;
+						h = image_aspect*size / 2.0f;
+					}
+					else {
+						w = image_aspect*size / 2.0f;
+						h = (float)size / 2.0f;
+					}
+
+					E = -w * co + h * si;
+					F = -h * co - w * si;
+
+					if ((i % 2) == (j % 2)) {
+						G = -w * co - h * si;
+						H = h * co - w * si;
+					}
+					else {
+						G = w * co + h * si;
+						H = -h * co + w * si;
+					}
+
+					I = F - H;
+					J = G - E;
+					K = G * F - E * H;
+
+					S = (dx * I + dy * J + K) / (-w * I - h * J);
+
+					scale = min_ff(scale, S);
+				}
+			}
 		}
 	}
+
+	stab->scale = scale;
+
+	if (stab->maxscale > 0.0f) {
+		stab->scale = max_ff(stab->scale, 1.0f / stab->maxscale);
+	}
+}
+
+
+/* Prepare working data and determine reference point for each track.
+ *
+ * NOTE: These calculations _could_ be cached and reused for all frames of the
+ *       same clip. However, since proper initialization depends on (weight)
+ *       animation and setup of tracks, ensuring consistency of cached init data
+ *       turns out to be tricky, hard to maintain and generally not worth the
+ *       effort. Thus we'll re-initialize on every frame.
+ */
+static StabContext *init_stabilizer(MovieClip *clip, int width, int height)
+{
+	MovieTracking *tracking = &clip->tracking;
+	MovieTrackingStabilization *stab = &tracking->stabilization;
+	float pixel_aspect = tracking->camera.pixel_aspect;
+	float aspect = (float)width * pixel_aspect / height;
+	int size = height;
+
+	StabContext *ctx = initialize_stabilization_working_context(clip);
+	BLI_assert(ctx != NULL);
+	initialize_all_tracks(ctx, aspect);
+	if (stab->flag & TRACKING_AUTOSCALE) {
+		stabilization_determine_safe_image_area(ctx, size, aspect);
+	}
+	/* By default, just use values for the global current frame. */
+	use_values_from_fcurves(ctx, false);
+	return ctx;
+}
+
+
+/* === public interface functions === */
+
+/* Get stabilization data (translation, scaling and angle) for a given frame.
+ * Returned data describes how to compensate the detected movement, but with any
+ * chosen scale factor already applied and any target frame position already
+ * compensated. In case stabilization fails or is disabled, neutral values are
+ * returned.
+ *
+ * framenr is a frame number, relative to the clip (not relative to the scene
+ *         timeline)
+ * width is an effective width of the canvas (square pixels), used to scale the
+ *       determined translation
+ *
+ * Outputs:
+ * - translation of the lateral shift, absolute canvas coordinates
+ *   (square pixels).
+ * - scale of the scaling to apply
+ * - angle of the rotation angle, relative to the frame center
+ */
+/* TODO(sergey): Use r_ prefix for output parameters here. */
+void BKE_tracking_stabilization_data_get(MovieClip *clip,
+                                         int framenr,
+                                         int width,
+                                         int height,
+                                         float translation[2],
+                                         float *scale,
+                                         float *angle)
+{
+	StabContext *ctx = NULL;
+	MovieTracking *tracking = &clip->tracking;
+	bool enabled = (tracking->stabilization.flag & TRACKING_2D_STABILIZATION);
+	/* Might become a parameter of a stabilization compositor node. */
+	bool do_compensate = true;
+	float scale_step = 0.0f;
+	float pixel_aspect = tracking->camera.pixel_aspect;
+	float aspect = (float)width * pixel_aspect / height;
+	int size = height;
+
+	if (enabled) {
+		ctx = init_stabilizer(clip, width, height);
+	}
+
+	if (enabled &&
+		stabilization_determine_offset_for_frame(ctx,
+		                                         framenr,
+		                                         aspect,
+		                                         translation,
+		                                         angle,
+		                                         &scale_step))
+	{
+		stabilization_calculate_data(ctx,
+		                             framenr,
+		                             size,
+		                             aspect,
+		                             do_compensate,
+		                             scale_step,
+		                             translation,
+		                             scale,
+		                             angle);
+	}
 	else {
 		zero_v2(translation);
 		*scale = 1.0f;
 		*angle = 0.0f;
 	}
+	discard_stabilization_working_context(ctx);
 }
 
-/* Stabilize given image buffer using stabilization data for
- * a specified frame number.
+/* Stabilize given image buffer using stabilization data for a specified
+ * frame number.
  *
- * NOTE: frame number should be in clip space, not scene space
+ * NOTE: frame number should be in clip space, not scene space.
  */
-ImBuf *BKE_tracking_stabilize_frame(MovieTracking *tracking, int framenr, ImBuf *ibuf,
-                                    float translation[2], float *scale, float *angle)
+/* TODO(sergey): Use r_ prefix for output parameters here. */
+ImBuf *BKE_tracking_stabilize_frame(MovieClip *clip,
+                                    int framenr,
+                                    ImBuf *ibuf,
+                                    float translation[2],
+                                    float *scale,
+                                    float *angle)
 {
 	float tloc[2], tscale, tangle;
+	MovieTracking *tracking = &clip->tracking;
 	MovieTrackingStabilization *stab = &tracking->stabilization;
 	ImBuf *tmpibuf;
 	int width = ibuf->x, height = ibuf->y;
-	float aspect = tracking->camera.pixel_aspect;
+	float pixel_aspect = tracking->camera.pixel_aspect;
 	float mat[4][4];
 	int j, filter = tracking->stabilization.filter;
 	void (*interpolation)(struct ImBuf *, struct ImBuf *, float, float, int, int) = NULL;
@@ -349,8 +1363,12 @@ ImBuf *BKE_tracking_stabilize_frame(MovieTracking *tracking, int framenr, ImBuf
 	tmpibuf = IMB_allocImBuf(ibuf->x, ibuf->y, ibuf->planes, ibuf_flags);
 
 	/* Calculate stabilization matrix. */
-	BKE_tracking_stabilization_data_get(tracking, framenr, width, height, tloc, &tscale, &tangle);
-	BKE_tracking_stabilization_data_to_mat4(ibuf->x, ibuf->y, aspect, tloc, tscale, tangle, mat);
+	BKE_tracking_stabilization_data_get(clip, framenr, width, height, tloc, &tscale, &tangle);
+	BKE_tracking_stabilization_data_to_mat4(ibuf->x, ibuf->y, pixel_aspect, tloc, tscale, tangle, mat);
+
+	/* The following code visits each nominal target grid position
+	 * and picks interpolated data "backwards" from source.
+	 * thus we need the inverse of the transformation to apply. */
 	invert_m4(mat);
 
 	if (filter == TRACKING_FILTER_NEAREST)
@@ -397,48 +1415,61 @@ ImBuf *BKE_tracking_stabilize_frame(MovieTracking *tracking, int framenr, ImBuf
 	return tmpibuf;
 }
 
-/* Get 4x4 transformation matrix which corresponds to
- * stabilization data and used for easy coordinate
- * transformation.
+
+/* Build a 4x4 transformation matrix based on the given 2D stabilization data.
+ * mat is a 4x4 matrix in homogeneous coordinates, adapted to the
+ *     final image buffer size and compensated for pixel aspect ratio,
+ *     ready for direct OpenGL drawing.
  *
- * NOTE: The reason it is 4x4 matrix is because it's
- *       used for OpenGL drawing directly.
+ * TODO(sergey): The signature of this function should be changed. we actually
+ *               don't need the dimensions of the image buffer. Instead we
+ *               should consider to provide the pivot point of the rotation as a
+ *               further stabilization data parameter.
  */
-void BKE_tracking_stabilization_data_to_mat4(int width, int height, float aspect,
+void BKE_tracking_stabilization_data_to_mat4(int buffer_width,
+                                             int buffer_height,
+                                             float pixel_aspect,
                                              float translation[2], float scale, float angle,
                                              float mat[4][4])
 {
 	float translation_mat[4][4], rotation_mat[4][4], scale_mat[4][4],
-	      center_mat[4][4], inv_center_mat[4][4],
+	      pivot_mat[4][4], inv_pivot_mat[4][4],
 	      aspect_mat[4][4], inv_aspect_mat[4][4];
-	float scale_vector[3] = {scale, scale, scale};
+	float scale_vector[3] = {scale, scale, 1.0f};
+
+	float pivot[2]; /* XXX this should be a parameter, it is part of the stabilization data */
+
+	/* Use the motion compensated image center as rotation center.
+	 * This is not 100% correct, but reflects the way the rotation data was
+	 * measured. Actually we'd need a way to find a good pivot, and use that
+	 * both for averaging and for compensation.
+	 */
+	/* TODO(sergey) pivot shouldn't be calculated here, rather received
+	 * as a parameter.
+	 */
+	pivot[0] = pixel_aspect * buffer_width / 2.0f - translation[0];
+	pivot[1] = (float)buffer_height        / 2.0f - translation[1];
 
 	unit_m4(translation_mat);
 	unit_m4(rotation_mat);
 	unit_m4(scale_mat);
-	unit_m4(center_mat);
 	unit_m4(aspect_mat);
+	unit_m4(pivot_mat);
+	unit_m4(inv_pivot_mat);
 
 	/* aspect ratio correction matrix */
-	aspect_mat[0][0] = 1.0f / aspect;
+	aspect_mat[0][0] /= pixel_aspect;
 	invert_m4_m4(inv_aspect_mat, aspect_mat);
 
-	/* image center as rotation center
-	 *
-	 * Rotation matrix is constructing in a way rotation happens around image center,
-	 * and it's matter of calculating translation in a way, that applying translation
-	 * after rotation would make it so rotation happens around median point of tracks
-	 * used for translation stabilization.
-	 */
-	center_mat[3][0] = (float)width / 2.0f;
-	center_mat[3][1] = (float)height / 2.0f;
-	invert_m4_m4(inv_center_mat, center_mat);
+	add_v2_v2(pivot_mat[3],     pivot);
+	sub_v2_v2(inv_pivot_mat[3], pivot);
 
 	size_to_mat4(scale_mat, scale_vector);       /* scale matrix */
 	add_v2_v2(translation_mat[3], translation);  /* translation matrix */
 	rotate_m4(rotation_mat, 'Z', angle);         /* rotation matrix */
 
 	/* compose transformation matrix */
-	mul_m4_series(mat, translation_mat, center_mat, aspect_mat, rotation_mat, inv_aspect_mat,
-	             scale_mat, inv_center_mat);
+	mul_m4_series(mat, aspect_mat, translation_mat,
+	                   pivot_mat, scale_mat, rotation_mat, inv_pivot_mat,
+	                   inv_aspect_mat);
 }