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, 83 insertions, 33 deletions

diff --git a/source/blender/compositor/operations/COM_MapUVOperation.cpp b/source/blender/compositor/operations/COM_MapUVOperation.cpp
index 289b447dec7..292f073548a 100644
--- a/source/blender/compositor/operations/COM_MapUVOperation.cpp
+++ b/source/blender/compositor/operations/COM_MapUVOperation.cpp
@@ -42,46 +42,28 @@ void MapUVOperation::initExecution()
 
 void MapUVOperation::executePixelSampled(float output[4], float x, float y, PixelSampler sampler)
 {
-	float inputUV[4];
-	float uv_a[4], uv_b[4];
-	float u, v;
+	float xy[2] = { x, y };
+	float uv[2], deriv[2][2], alpha;
 
-	float dx, dy;
-	float uv_l, uv_r;
-	float uv_u, uv_d;
-
-	this->m_inputUVProgram->readSampled(inputUV, x, y, sampler);
-	if (inputUV[2] == 0.f) {
+	pixelTransform(xy, uv, deriv, alpha);
+	if (alpha == 0.0f) {
 		zero_v4(output);
 		return;
 	}
-	/* adaptive sampling, red (U) channel */
-	this->m_inputUVProgram->readSampled(uv_a, x - 1, y, COM_PS_NEAREST);
-	this->m_inputUVProgram->readSampled(uv_b, x + 1, y, COM_PS_NEAREST);
-	uv_l = uv_a[2] != 0.f ? fabsf(inputUV[0] - uv_a[0]) : 0.f;
-	uv_r = uv_b[2] != 0.f ? fabsf(inputUV[0] - uv_b[0]) : 0.f;
-
-	dx = 0.5f * (uv_l + uv_r);
-
-	/* adaptive sampling, green (V) channel */
-	this->m_inputUVProgram->readSampled(uv_a, x, y - 1, COM_PS_NEAREST);
-	this->m_inputUVProgram->readSampled(uv_b, x, y + 1, COM_PS_NEAREST);
-	uv_u = uv_a[2] != 0.f ? fabsf(inputUV[1] - uv_a[1]) : 0.f;
-	uv_d = uv_b[2] != 0.f ? fabsf(inputUV[1] - uv_b[1]) : 0.f;
-
-	dy = 0.5f * (uv_u + uv_d);
 
+	/* EWA filtering */
+	this->m_inputColorProgram->readFiltered(output, uv[0], uv[1], deriv[0], deriv[1], COM_PS_BILINEAR);
+	
 	/* UV to alpha threshold */
 	const float threshold = this->m_alpha * 0.05f;
-	float alpha = 1.0f - threshold * (dx + dy);
-	if (alpha < 0.f) alpha = 0.f;
-	else alpha *= inputUV[2];
-
-	/* EWA filtering */
-	u = inputUV[0] * this->m_inputColorProgram->getWidth();
-	v = inputUV[1] * this->m_inputColorProgram->getHeight();
-
-	this->m_inputColorProgram->readFiltered(output, u, v, dx, dy, COM_PS_NEAREST);
+	/* XXX alpha threshold is used to fade out pixels on boundaries with invalid derivatives.
+	 * this calculation is not very well defined, should be looked into if it becomes a problem ...
+	 */
+	float du = len_v2(deriv[0]);
+	float dv = len_v2(deriv[1]);
+	float factor = 1.0f - threshold * (du + dv);
+	if (factor < 0.f) alpha = 0.f;
+	else alpha *= factor;
 
 	/* "premul" */
 	if (alpha < 1.0f) {
@@ -89,6 +71,74 @@ void MapUVOperation::executePixelSampled(float output[4], float x, float y, Pixe
 	}
 }
 
+bool MapUVOperation::read_uv(float x, float y, float &r_u, float &r_v, float &r_alpha)
+{
+	float width = m_inputUVProgram->getWidth();
+	float height = m_inputUVProgram->getHeight();
+	if (x < 0.0f || x >= width || y < 0.0f || y >= height) {
+		r_u = 0.0f;
+		r_v = 0.0f;
+		r_alpha = 0.0f;
+		return false;
+	}
+	else {
+		float col[4];
+		m_inputUVProgram->readSampled(col, x, y, COM_PS_BILINEAR);
+		r_u = col[0] * width;
+		r_v = col[1] * height;
+		r_alpha = col[2];
+		return true;
+	}
+}
+
+void MapUVOperation::pixelTransform(const float xy[2], float r_uv[2], float r_deriv[2][2], float &r_alpha)
+{
+	float uv[2], alpha; /* temporary variables for derivative estimation */
+	int num;
+
+	read_uv(xy[0], xy[1], r_uv[0], r_uv[1], r_alpha);
+
+	/* 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_uv(xy[0] + epsilon[0], xy[1], uv[0], uv[1], alpha)) {
+		r_deriv[0][0] += uv[0] - r_uv[0];
+		r_deriv[1][0] += uv[1] - r_uv[1];
+		++num;
+	}
+	if (read_uv(xy[0] - epsilon[0], xy[1], uv[0], uv[1], alpha)) {
+		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;
+	}
+
+	num = 0;
+	if (read_uv(xy[0], xy[1] + epsilon[1], uv[0], uv[1], alpha)) {
+		r_deriv[0][1] += uv[0] - r_uv[0];
+		r_deriv[1][1] += uv[1] - r_uv[1];
+		++num;
+	}
+	if (read_uv(xy[0], xy[1] - epsilon[1], uv[0], uv[1], alpha)) {
+		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 MapUVOperation::deinitExecution()
 {
 	this->m_inputUVProgram = NULL;