#version 450 core
-in vec2 tc;
+/*
+ The motion search is one of the two major components of DIS. It works more or less
+ like you'd expect; there's a bunch of overlapping patches (8x8 or 12x12 pixels) in
+ a grid, and for each patch, there's a search to try to find the most similar patch
+ in the other frame.
+
+ Unlike in a typical video codec, the DIS patch search is based on gradient descent;
+ conceptually, you start with an initial guess (the value from the previous level,
+ or the zero flow for the very first level), subtract the reference (“template”)
+ patch from the candidate, look at the gradient to see in what direction there is
+ a lower difference, and then inch a bit toward that direction. (There is seemingly
+ nothing like AdaM, Momentum or similar, but the searched value is only in two
+ dimensions, so perhaps it doesn't matter as much then.)
+
+ DIS does a tweak to this concept. Since the procedure as outlined above requires
+ computing the gradient of the candidate patch, it uses the reference patch as
+ candidate (thus the “inverse” name), and thus uses _its_ gradient to understand
+ in which direction to move. (This is a bit dodgy, but not _that_ dodgy; after
+ all, the two patches are supposed to be quite similar, so their surroundings and
+ thus also gradients should also be quite similar.) It's not entirely clear whether
+ this is still a win on GPU, where calculations are much cheaper, especially
+ the way we parallelize the search, but we've kept it around for now.
+
+ The inverse search is explained and derived in the supplementary material of the
+ paper, section A. Do note that there's a typo; the text under equation 9 claims
+ that the matrix H is n x n (where presumably n is the patch size), while in reality,
+ it's 2x2.
+
+ Our GPU parallellization is fairly dumb right now; we do one patch per fragment
+ (ie., parallellize only over patches, not within each patch), which may not
+ be optimal. In particular, in the initial level, we only have 40 patches,
+ which is on the low side for a GPU, and the memory access patterns may also not
+ be ideal.
+ */
+
+const uint patch_size = 12;
+const uint num_iterations = 16;
+
+in vec2 flow_tc;
+in vec2 patch_bottom_left_texel; // Center of bottom-left texel of patch.
out vec2 out_flow;
-uniform sampler2D tex;
+uniform sampler2D flow_tex, grad0_tex, image0_tex, image1_tex;
+uniform float image_width, image_height, inv_image_width, inv_image_height;
void main()
{
-// out_flow = texture(tex, tc).xy;
- out_flow = tc.xy;
+ // Lock patch_bottom_left_texel to an integer, so that we never get
+ // any bilinear artifacts for the gradient.
+ vec2 base = round(patch_bottom_left_texel * vec2(image_width, image_height))
+ * vec2(inv_image_width, inv_image_height);
+
+ // First, precompute the pseudo-Hessian for the template patch.
+ // This is the part where we really save by the inverse search
+ // (ie., we can compute it up-front instead of anew for each
+ // patch).
+ //
+ // H = sum(S^T S)
+ //
+ // where S is the gradient at each point in the patch. Note that
+ // this is an outer product, so we get a (symmetric) 2x2 matrix,
+ // not a scalar.
+ mat2 H = mat2(0.0f);
+ for (uint y = 0; y < patch_size; ++y) {
+ for (uint x = 0; x < patch_size; ++x) {
+ vec2 tc;
+ tc.x = base.x + x * inv_image_width;
+ tc.y = base.y + y * inv_image_height;
+ vec2 grad = texture(grad0_tex, tc).xy;
+ H[0][0] += grad.x * grad.x;
+ H[1][1] += grad.y * grad.y;
+ H[0][1] += grad.x * grad.y;
+ }
+ }
+ H[1][0] = H[0][1];
+
+ // Make sure we don't get a singular matrix even if e.g. the picture is
+ // all black. (The paper doesn't mention this, but the reference code
+ // does it, and it seems like a reasonable hack to avoid NaNs. With such
+ // a H, we'll go out-of-bounds pretty soon, though.)
+ if (determinant(H) < 1e-6) {
+ H[0][0] += 1e-6;
+ H[1][1] += 1e-6;
+ }
+
+ mat2 H_inv = inverse(H);
+
+ // Fetch the initial guess for the flow.
+ vec2 initial_u = texture(flow_tex, flow_tc).xy;
+ vec2 u = initial_u;
+
+ for (uint i = 0; i < num_iterations; ++i) {
+ vec2 du = vec2(0.0, 0.0);
+ for (uint y = 0; y < patch_size; ++y) {
+ for (uint x = 0; x < patch_size; ++x) {
+ vec2 tc;
+ tc.x = base.x + x * inv_image_width;
+ tc.y = base.y + y * inv_image_height;
+ vec2 grad = texture(grad0_tex, tc).xy;
+ float t = texture(image0_tex, tc).x;
+ float warped = texture(image1_tex, tc + u).x;
+ du += grad * (warped - t);
+ }
+ }
+ u += H_inv * du * vec2(inv_image_width, inv_image_height);
+ }
+
+ // TODO: reject if moving too far
+
+ out_flow = u;
}
projects / nageru / blobdiff