Fix for EWA (elliptical weighted average) sampling in the compositor.

EWA sampling is designed for downsampling images, i.e. scaling down the size of
input image pixels, which happens regularly in compositing. While the standard
sampling methods (linear, cubic) work reasonably well for linear
transformations, they don't yield good results in non-linear cases like
perspective projection or arbitrary displacement. EWA sampling is comparable to
mipmapping, but avoids problems with discontinuities.

To work correctly the EWA algorithm needs partial derivatives of the mapping
functions which convert output pixel coordinates back into the input image
space (2x2 Jacobian matrix). With these derivatives the EWA algorithm
projects ellipses into the input space and accumulates colors over their
area. This calculation was not done correctly in the compositor, only the
derivatives du/dx and dv/dy were calculation, basically this means it only
worked for non-rotated input images.

The patch introduces full derivative calculations du/dx, du/dy, dv/dx, dv/dy for
the 3 nodes which use EWA sampling currently: PlaneTrackWarp, MapUV and
Displace. In addition the calculation of ellipsis area and axis-aligned
bounding boxes has been fixed.

For the MapUV and Displace nodes the derivatives have to be estimated by
evaluating the UV/displacement inputs with 1-pixel offsets, which can still have
problems on discontinuities and sub-pixel variations. These potential problems
can only be alleviated by more radical design changes in the compositor
functions, which are out of scope for now. Basically the values passed to the
UV/Displacement inputs would need to be associated with their 1st order
derivatives, which requires a general approach to derivatives in all nodes.

1 files changed, 81 insertions, 43 deletions

diff --git a/source/blender/compositor/operations/COM_DisplaceOperation.cpp b/source/blender/compositor/operations/COM_DisplaceOperation.cpp
index 17692bd18ef..96031e7acc4 100644
--- a/source/blender/compositor/operations/COM_DisplaceOperation.cpp
+++ b/source/blender/compositor/operations/COM_DisplaceOperation.cpp
@@ -49,54 +49,92 @@ void DisplaceOperation::initExecution()
 	this->m_height_x4 = this->getHeight() * 4;
 }
 
-
-/* minimum distance (in pixels) a pixel has to be displaced
- * in order to take effect */
-#define DISPLACE_EPSILON    0.01f
-
-void DisplaceOperation::executePixel(float output[4], int x, int y, void *data)
+void DisplaceOperation::executePixelSampled(float output[4], float x, float y, PixelSampler sampler)
 {
-	float inVector[4];
-	float inScale[4];
+	float xy[2] = { x, y };
+	float uv[2], deriv[2][2];
 
-	float p_dx, p_dy;   /* main displacement in pixel space */
-	float d_dx, d_dy;
-	float dxt, dyt;
-	float u, v;
+	pixelTransform(xy, uv, deriv);
 
-	this->m_inputScaleXProgram->readSampled(inScale, x, y, COM_PS_NEAREST);
-	float xs = inScale[0];
-	this->m_inputScaleYProgram->readSampled(inScale, x, y, COM_PS_NEAREST);
-	float ys = inScale[0];
+	/* EWA filtering (without nearest it gets blurry with NO distortion) */
+	this->m_inputColorProgram->readFiltered(output, uv[0], uv[1], deriv[0], deriv[1], COM_PS_BILINEAR);
+}
 
+bool DisplaceOperation::read_displacement(float x, float y, float xscale, float yscale, const float origin[2], float &r_u, float &r_v)
+{
+	float width = m_inputVectorProgram->getWidth();
+	float height = m_inputVectorProgram->getHeight();
+	if (x < 0.0f || x >= width || y < 0.0f || y >= height) {
+		r_u = 0.0f;
+		r_v = 0.0f;
+		return false;
+	}
+	else {
+		float col[4];
+		m_inputVectorProgram->readSampled(col, x, y, COM_PS_BILINEAR);
+		r_u = origin[0] - col[0]*xscale + 0.5f;
+		r_v = origin[1] - col[1]*yscale + 0.5f;
+		return true;
+	}
+}
+
+void DisplaceOperation::pixelTransform(const float xy[2], float r_uv[2], float r_deriv[2][2])
+{
+	float col[4];
+	float uv[2]; /* temporary variables for derivative estimation */
+	int num;
+
+	m_inputScaleXProgram->readSampled(col, xy[0], xy[1], COM_PS_NEAREST);
+	float xs = col[0];
+	m_inputScaleYProgram->readSampled(col, xy[0], xy[1], COM_PS_NEAREST);
+	float ys = col[0];
 	/* clamp x and y displacement to triple image resolution - 
 	 * to prevent hangs from huge values mistakenly plugged in eg. z buffers */
-	CLAMP(xs, -this->m_width_x4, this->m_width_x4);
-	CLAMP(ys, -this->m_height_x4, this->m_height_x4);
-
-	this->m_inputVectorProgram->readSampled(inVector, x, y, COM_PS_NEAREST);
-	p_dx = inVector[0] * xs;
-	p_dy = inVector[1] * ys;
+	CLAMP(xs, -m_width_x4, m_width_x4);
+	CLAMP(ys, -m_height_x4, m_height_x4);
 
 	/* displaced pixel in uv coords, for image sampling */
-	u = x - p_dx + 0.5f;
-	v = y - p_dy + 0.5f;
-
-	/* calc derivatives */
-	this->m_inputVectorProgram->readSampled(inVector, x + 1, y, COM_PS_NEAREST);
-	d_dx = inVector[0] * xs;
-	this->m_inputVectorProgram->readSampled(inVector, x, y + 1, COM_PS_NEAREST);
-	d_dy = inVector[1] * ys;
-
-	/* clamp derivatives to minimum displacement distance in UV space */
-	dxt = p_dx - d_dx;
-	dyt = p_dy - d_dy;
-
-	dxt = signf(dxt) * max_ff(fabsf(dxt), DISPLACE_EPSILON) / this->getWidth();
-	dyt = signf(dyt) * max_ff(fabsf(dyt), DISPLACE_EPSILON) / this->getHeight();
+	read_displacement(xy[0], xy[1], xs, ys, xy, r_uv[0], r_uv[1]);
+
+	/* Estimate partial derivatives using 1-pixel offsets */
+	const float epsilon[2] = { 1.0f, 1.0f };
+	
+	zero_v2(r_deriv[0]);
+	zero_v2(r_deriv[1]);
+
+	num = 0;
+	if (read_displacement(xy[0] + epsilon[0], xy[1], xs, ys, xy, uv[0], uv[1])) {
+		r_deriv[0][0] += uv[0] - r_uv[0];
+		r_deriv[1][0] += uv[1] - r_uv[1];
+		++num;
+	}
+	if (read_displacement(xy[0] - epsilon[0], xy[1], xs, ys, xy, uv[0], uv[1])) {
+		r_deriv[0][0] += r_uv[0] - uv[0];
+		r_deriv[1][0] += r_uv[1] - uv[1];
+		++num;
+	}
+	if (num > 0) {
+		float numinv = 1.0f / (float)num;
+		r_deriv[0][0] *= numinv;
+		r_deriv[1][0] *= numinv;
+	}
 
-	/* EWA filtering (without nearest it gets blurry with NO distortion) */
-	this->m_inputColorProgram->readFiltered(output, u, v, dxt, dyt, COM_PS_NEAREST);
+	num = 0;
+	if (read_displacement(xy[0], xy[1] + epsilon[1], xs, ys, xy, uv[0], uv[1])) {
+		r_deriv[0][1] += uv[0] - r_uv[0];
+		r_deriv[1][1] += uv[1] - r_uv[1];
+		++num;
+	}
+	if (read_displacement(xy[0], xy[1] - epsilon[1], xs, ys, xy, uv[0], uv[1])) {
+		r_deriv[0][1] += r_uv[0] - uv[0];
+		r_deriv[1][1] += r_uv[1] - uv[1];
+		++num;
+	}
+	if (num > 0) {
+		float numinv = 1.0f / (float)num;
+		r_deriv[0][1] *= numinv;
+		r_deriv[1][1] *= numinv;
+	}
 }
 
 void DisplaceOperation::deinitExecution()
@@ -126,10 +164,10 @@ bool DisplaceOperation::determineDependingAreaOfInterest(rcti *input, ReadBuffer
 
 	/* vector */
 	operation = getInputOperation(1);
-	vectorInput.xmax = input->xmax + 2;
-	vectorInput.xmin = input->xmin;
-	vectorInput.ymax = input->ymax + 2;
-	vectorInput.ymin = input->ymin;
+	vectorInput.xmax = input->xmax + 1;
+	vectorInput.xmin = input->xmin - 1;
+	vectorInput.ymax = input->ymax + 1;
+	vectorInput.ymin = input->ymin - 1;
 	if (operation->determineDependingAreaOfInterest(&vectorInput, readOperation, output)) {
 		return true;
 	}