X-Git-Url: https://git.sesse.net/?a=blobdiff_plain;ds=sidebyside;f=resample_effect.cpp;h=f438a873b095114554bb1b53a41cebe263d16f4b;hb=0af958592e20bde3721a6deb16a6e32edfeb6cdc;hp=f4808c4560437288a327156f10a2f0e794e1f991;hpb=c62391987241f1482a99b6f6417fbec1d0ef2344;p=movit diff --git a/resample_effect.cpp b/resample_effect.cpp index f4808c4..f438a87 100644 --- a/resample_effect.cpp +++ b/resample_effect.cpp @@ -7,6 +7,9 @@ #include #include #include +#include +#include +#include #include "effect_chain.h" #include "effect_util.h" @@ -15,6 +18,7 @@ #include "resample_effect.h" #include "util.h" +using namespace Eigen; using namespace std; namespace movit { @@ -113,6 +117,22 @@ unsigned combine_samples(const Tap *src, Tap *dst, unsigned sr return num_samples_saved; } +// Normalize so that the sum becomes one. Note that we do it twice; +// this sometimes helps a tiny little bit when we have many samples. +template +void normalize_sum(Tap* vals, unsigned num) +{ + for (int normalize_pass = 0; normalize_pass < 2; ++normalize_pass) { + double sum = 0.0; + for (unsigned i = 0; i < num; ++i) { + sum += to_fp64(vals[i].weight); + } + for (unsigned i = 0; i < num; ++i) { + vals[i].weight = from_fp64(to_fp64(vals[i].weight) / sum); + } + } +} + // Make use of the bilinear filtering in the GPU to reduce the number of samples // we need to make. This is a bit more complex than BlurEffect since we cannot combine // two neighboring samples if their weights have differing signs, so we first need to @@ -141,19 +161,7 @@ unsigned combine_many_samples(const Tap *weights, unsigned src_size, unsi src_samples, src_samples - src_bilinear_samples); assert(int(src_samples) - int(num_samples_saved) == src_bilinear_samples); - - // Normalize so that the sum becomes one. Note that we do it twice; - // this sometimes helps a tiny little bit when we have many samples. - for (int normalize_pass = 0; normalize_pass < 2; ++normalize_pass) { - double sum = 0.0; - for (int i = 0; i < src_bilinear_samples; ++i) { - sum += to_fp64(bilinear_weights_ptr[i].weight); - } - for (int i = 0; i < src_bilinear_samples; ++i) { - bilinear_weights_ptr[i].weight = from_fp64( - to_fp64(bilinear_weights_ptr[i].weight) / sum); - } - } + normalize_sum(bilinear_weights_ptr, src_bilinear_samples); } return src_bilinear_samples; } @@ -216,6 +224,112 @@ double compute_sum_sq_error(const Tap* weights, unsigned num_weights, return sum_sq_error; } +// Given a predefined, fixed set of bilinear weight positions, try to optimize +// their weights through some linear algebra. This can do a better job than +// the weight calculation in combine_samples() because it can look at the entire +// picture (an effective weight can sometimes be affected by multiple samples). +// It will also optimize weights for non-combined samples, which is useful when +// a sample happens in-between texels for numerical reasons. +// +// The math goes as follows: The desired result is a weighted sum, where the +// weights are the coefficients in : +// +// y = sum(c_j x_j, j) +// +// We try to approximate this by a different set of coefficients, which have +// weights d_i and are placed at some fraction to the right of a source texel x_j. +// This means it will influence two texels (x_j and x_{j+1}); generalizing this, +// let us define that w_ij means the amount texel influences bilinear weight +// (keeping in mind that w_ij = 0 for all but at most two different j). +// This means the actually computed result is: +// +// y' = sum(d_i w_ij x_j, j) +// +// We assume w_ij fixed and wish to find {d_i} so that y' gets as close to y +// as possible. Specifically, let us consider the sum of squred errors of the +// coefficients: +// +// ε² = sum((sum( d_i w_ij, i ) - c_j)², j) +// +// The standard trick, which also applies just fine here, is to differentiate +// the error with respect to each variable we wish to optimize, and set each +// such expression to zero. Solving this equation set (which we can do efficiently +// by letting Eigen invert a sparse matrix for us) yields the minimum possible +// error. To see the form each such equation takes, pick any value k and +// differentiate the expression by d_k: +// +// ∂(ε²)/∂(d_k) = sum(2(sum( d_i w_ij, i ) - c_j) w_kj, j) +// +// Setting this expression equal to zero, dropping the irrelevant factor 2 and +// rearranging yields: +// +// sum(w_kj sum( d_i w_ij, i ), j) = sum(w_kj c_j, j) +// +// where again, we remember where the sums over j are over at most two elements, +// since w_kj is nonzero for at most two values of j. +template +void optimize_sum_sq_error(const Tap* weights, unsigned num_weights, + Tap* bilinear_weights, unsigned num_bilinear_weights, + unsigned size) +{ + // Find the range of the desired weights. + int c_lower_pos = lrintf(weights[0].pos * size - 0.5); + int c_upper_pos = lrintf(weights[num_weights - 1].pos * size - 0.5) + 1; + + SparseMatrix A(num_bilinear_weights, num_bilinear_weights); + SparseVector b(num_bilinear_weights); + + // Convert each bilinear weight to the (x, frac) form for less junk in the code below. + int* pos = new int[num_bilinear_weights]; + float* fracs = new float[num_bilinear_weights]; + for (unsigned i = 0; i < num_bilinear_weights; ++i) { + const float pixel_pos = to_fp64(bilinear_weights[i].pos) * size - 0.5f; + const float f = pixel_pos - floor(pixel_pos); + pos[i] = int(floor(pixel_pos)); + fracs[i] = lrintf(f / movit_texel_subpixel_precision) * movit_texel_subpixel_precision; + } + + // The index ordering is a bit unusual to fit better with the + // notation in the derivation above. + for (unsigned k = 0; k < num_bilinear_weights; ++k) { + for (int j = pos[k]; j <= pos[k] + 1; ++j) { + const float w_kj = (j == pos[k]) ? (1.0f - fracs[k]) : fracs[k]; + for (unsigned i = 0; i < num_bilinear_weights; ++i) { + float w_ij; + if (j == pos[i]) { + w_ij = 1.0f - fracs[i]; + } else if (j == pos[i] + 1) { + w_ij = fracs[i]; + } else { + // w_ij = 0 + continue; + } + A.coeffRef(i, k) += w_kj * w_ij; + } + float c_j; + if (j >= c_lower_pos && j < c_upper_pos) { + c_j = weights[j - c_lower_pos].weight; + } else { + c_j = 0.0f; + } + b.coeffRef(k) += w_kj * c_j; + } + } + delete[] pos; + delete[] fracs; + + A.makeCompressed(); + SparseQR, COLAMDOrdering > qr(A); + assert(qr.info() == Success); + SparseMatrix new_weights = qr.solve(b); + assert(qr.info() == Success); + + for (unsigned i = 0; i < num_bilinear_weights; ++i) { + bilinear_weights[i].weight = from_fp64(new_weights.coeff(i, 0)); + } + normalize_sum(bilinear_weights, num_bilinear_weights); +} + } // namespace ResampleEffect::ResampleEffect() @@ -508,6 +622,10 @@ void SingleResamplePassEffect::update_texture(GLuint glsl_program_num, const str bool fallback_to_fp32 = false; double max_sum_sq_error_fp16 = 0.0; for (unsigned y = 0; y < dst_samples; ++y) { + optimize_sum_sq_error( + weights + y * src_samples, src_samples, + bilinear_weights_fp16 + y * src_bilinear_samples, src_bilinear_samples, + src_size); double sum_sq_error_fp16 = compute_sum_sq_error( weights + y * src_samples, src_samples, bilinear_weights_fp16 + y * src_bilinear_samples, src_bilinear_samples, @@ -520,6 +638,12 @@ void SingleResamplePassEffect::update_texture(GLuint glsl_program_num, const str if (max_sum_sq_error_fp16 > 2.0f / (255.0f * 255.0f)) { fallback_to_fp32 = true; src_bilinear_samples = combine_many_samples(weights, src_size, src_samples, dst_samples, &bilinear_weights_fp32); + for (unsigned y = 0; y < dst_samples; ++y) { + optimize_sum_sq_error( + weights + y * src_samples, src_samples, + bilinear_weights_fp32 + y * src_bilinear_samples, src_bilinear_samples, + src_size); + } } // Encode as a two-component texture. Note the GL_REPEAT.