From 641053e9fc86b2166e361a983075febc3bb69acd Mon Sep 17 00:00:00 2001 From: "Steinar H. Gunderson" Date: Mon, 23 Feb 2015 01:19:03 +0100 Subject: [PATCH] Revert the optimization of the bilinear weights. For the case where the resampling changed every frame (e.g. a zoom), it just consumed too much CPU to be worth it, especially in memory management; this is painful because it was an elegant solution to a tricky problem, but it just has to go for now. Also drop out to fp32 at the first sight of too-high error. --- resample_effect.cpp | 126 +++----------------------------------------- 1 file changed, 7 insertions(+), 119 deletions(-) diff --git a/resample_effect.cpp b/resample_effect.cpp index f438a87..aa3a403 100644 --- a/resample_effect.cpp +++ b/resample_effect.cpp @@ -224,112 +224,6 @@ 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: -// -// ÎµÂ² = sum((sum( d_i w_ij, i ) - c_j)Â², 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: -// -// â(ÎµÂ²)/â(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() @@ -616,34 +510,28 @@ void SingleResamplePassEffect::update_texture(GLuint glsl_program_num, const str // Now make use of the bilinear filtering in the GPU to reduce the number of samples // we need to make. Try fp16 first; if it's not accurate enough, we go to fp32. + // Our tolerance level for total error is a bit higher than the one for invididual + // samples, since one would assume overall errors in the shape don't matter as much. + const float max_error = 2.0f / (255.0f * 255.0f); Tap *bilinear_weights_fp16; src_bilinear_samples = combine_many_samples(weights, src_size, src_samples, dst_samples, &bilinear_weights_fp16); Tap *bilinear_weights_fp32 = NULL; 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, src_size); max_sum_sq_error_fp16 = std::max(max_sum_sq_error_fp16, sum_sq_error_fp16); + if (max_sum_sq_error_fp16 > max_error) { + break; + } } - // Our tolerance level for total error is a bit higher than the one for invididual - // samples, since one would assume overall errors in the shape don't matter as much. - if (max_sum_sq_error_fp16 > 2.0f / (255.0f * 255.0f)) { + if (max_sum_sq_error_fp16 > max_error) { 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. -- 2.20.1