// basisu_ssim.cpp // Copyright (C) 2019 Binomial LLC. All Rights Reserved. // // Licensed under the Apache License, Version 2.0 (the "License"); // you may not use this file except in compliance with the License. // You may obtain a copy of the License at // // http://www.apache.org/licenses/LICENSE-2.0 // // Unless required by applicable law or agreed to in writing, software // distributed under the License is distributed on an "AS IS" BASIS, // WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. // See the License for the specific language governing permissions and // limitations under the License. #include "basisu_ssim.h" #ifndef M_PI #define M_PI 3.14159265358979323846 #endif namespace basisu { float gauss(int x, int y, float sigma_sqr) { float pow = expf(-((x * x + y * y) / (2.0f * sigma_sqr))); float g = (1.0f / (sqrtf((float)(2.0f * M_PI * sigma_sqr)))) * pow; return g; } // size_x/y should be odd void compute_gaussian_kernel(float *pDst, int size_x, int size_y, float sigma_sqr, uint32_t flags) { assert(size_x & size_y & 1); if (!(size_x | size_y)) return; int mid_x = size_x / 2; int mid_y = size_y / 2; double sum = 0; for (int x = 0; x < size_x; x++) { for (int y = 0; y < size_y; y++) { float g; if ((x > mid_x) && (y < mid_y)) g = pDst[(size_x - x - 1) + y * size_x]; else if ((x < mid_x) && (y > mid_y)) g = pDst[x + (size_y - y - 1) * size_x]; else if ((x > mid_x) && (y > mid_y)) g = pDst[(size_x - x - 1) + (size_y - y - 1) * size_x]; else g = gauss(x - mid_x, y - mid_y, sigma_sqr); pDst[x + y * size_x] = g; sum += g; } } if (flags & cComputeGaussianFlagNormalizeCenterToOne) { sum = pDst[mid_x + mid_y * size_x]; } if (flags & (cComputeGaussianFlagNormalizeCenterToOne | cComputeGaussianFlagNormalize)) { double one_over_sum = 1.0f / sum; for (int i = 0; i < size_x * size_y; i++) pDst[i] = static_cast(pDst[i] * one_over_sum); if (flags & cComputeGaussianFlagNormalizeCenterToOne) pDst[mid_x + mid_y * size_x] = 1.0f; } if (flags & cComputeGaussianFlagPrint) { printf("{\n"); for (int y = 0; y < size_y; y++) { printf(" "); for (int x = 0; x < size_x; x++) { printf("%f, ", pDst[x + y * size_x]); } printf("\n"); } printf("}"); } } void gaussian_filter(imagef &dst, const imagef &orig_img, uint32_t odd_filter_width, float sigma_sqr, bool wrapping, uint32_t width_divisor, uint32_t height_divisor) { assert(odd_filter_width && (odd_filter_width & 1)); odd_filter_width |= 1; vector2D kernel(odd_filter_width, odd_filter_width); compute_gaussian_kernel(kernel.get_ptr(), odd_filter_width, odd_filter_width, sigma_sqr, cComputeGaussianFlagNormalize); const int dst_width = orig_img.get_width() / width_divisor; const int dst_height = orig_img.get_height() / height_divisor; const int H = odd_filter_width / 2; const int L = -H; dst.crop(dst_width, dst_height); //#pragma omp parallel for for (int oy = 0; oy < dst_height; oy++) { for (int ox = 0; ox < dst_width; ox++) { vec4F c(0.0f); for (int yd = L; yd <= H; yd++) { int y = oy * height_divisor + (height_divisor >> 1) + yd; for (int xd = L; xd <= H; xd++) { int x = ox * width_divisor + (width_divisor >> 1) + xd; const vec4F &p = orig_img.get_clamped_or_wrapped(x, y, wrapping, wrapping); float w = kernel(xd + H, yd + H); c[0] += p[0] * w; c[1] += p[1] * w; c[2] += p[2] * w; c[3] += p[3] * w; } } dst(ox, oy).set(c[0], c[1], c[2], c[3]); } } } void pow_image(const imagef &src, imagef &dst, const vec4F &power) { dst.resize(src); //#pragma omp parallel for for (int y = 0; y < (int)dst.get_height(); y++) { for (uint32_t x = 0; x < dst.get_width(); x++) { const vec4F &p = src(x, y); if ((power[0] == 2.0f) && (power[1] == 2.0f) && (power[2] == 2.0f) && (power[3] == 2.0f)) dst(x, y).set(p[0] * p[0], p[1] * p[1], p[2] * p[2], p[3] * p[3]); else dst(x, y).set(powf(p[0], power[0]), powf(p[1], power[1]), powf(p[2], power[2]), powf(p[3], power[3])); } } } void mul_image(const imagef &src, imagef &dst, const vec4F &mul) { dst.resize(src); //#pragma omp parallel for for (int y = 0; y < (int)dst.get_height(); y++) { for (uint32_t x = 0; x < dst.get_width(); x++) { const vec4F &p = src(x, y); dst(x, y).set(p[0] * mul[0], p[1] * mul[1], p[2] * mul[2], p[3] * mul[3]); } } } void scale_image(const imagef &src, imagef &dst, const vec4F &scale, const vec4F &shift) { dst.resize(src); //#pragma omp parallel for for (int y = 0; y < (int)dst.get_height(); y++) { for (uint32_t x = 0; x < dst.get_width(); x++) { const vec4F &p = src(x, y); vec4F d; for (uint32_t c = 0; c < 4; c++) d[c] = scale[c] * p[c] + shift[c]; dst(x, y).set(d[0], d[1], d[2], d[3]); } } } void add_weighted_image(const imagef &src1, const vec4F &alpha, const imagef &src2, const vec4F &beta, const vec4F &gamma, imagef &dst) { dst.resize(src1); //#pragma omp parallel for for (int y = 0; y < (int)dst.get_height(); y++) { for (uint32_t x = 0; x < dst.get_width(); x++) { const vec4F &s1 = src1(x, y); const vec4F &s2 = src2(x, y); dst(x, y).set( s1[0] * alpha[0] + s2[0] * beta[0] + gamma[0], s1[1] * alpha[1] + s2[1] * beta[1] + gamma[1], s1[2] * alpha[2] + s2[2] * beta[2] + gamma[2], s1[3] * alpha[3] + s2[3] * beta[3] + gamma[3]); } } } void add_image(const imagef &src1, const imagef &src2, imagef &dst) { dst.resize(src1); //#pragma omp parallel for for (int y = 0; y < (int)dst.get_height(); y++) { for (uint32_t x = 0; x < dst.get_width(); x++) { const vec4F &s1 = src1(x, y); const vec4F &s2 = src2(x, y); dst(x, y).set(s1[0] + s2[0], s1[1] + s2[1], s1[2] + s2[2], s1[3] + s2[3]); } } } void adds_image(const imagef &src, const vec4F &value, imagef &dst) { dst.resize(src); //#pragma omp parallel for for (int y = 0; y < (int)dst.get_height(); y++) { for (uint32_t x = 0; x < dst.get_width(); x++) { const vec4F &p = src(x, y); dst(x, y).set(p[0] + value[0], p[1] + value[1], p[2] + value[2], p[3] + value[3]); } } } void mul_image(const imagef &src1, const imagef &src2, imagef &dst, const vec4F &scale) { dst.resize(src1); //#pragma omp parallel for for (int y = 0; y < (int)dst.get_height(); y++) { for (uint32_t x = 0; x < dst.get_width(); x++) { const vec4F &s1 = src1(x, y); const vec4F &s2 = src2(x, y); vec4F d; for (uint32_t c = 0; c < 4; c++) { float v1 = s1[c]; float v2 = s2[c]; d[c] = v1 * v2 * scale[c]; } dst(x, y) = d; } } } void div_image(const imagef &src1, const imagef &src2, imagef &dst, const vec4F &scale) { dst.resize(src1); //#pragma omp parallel for for (int y = 0; y < (int)dst.get_height(); y++) { for (uint32_t x = 0; x < dst.get_width(); x++) { const vec4F &s1 = src1(x, y); const vec4F &s2 = src2(x, y); vec4F d; for (uint32_t c = 0; c < 4; c++) { float v = s2[c]; if (v == 0.0f) d[c] = 0.0f; else d[c] = (s1[c] * scale[c]) / v; } dst(x, y) = d; } } } vec4F avg_image(const imagef &src) { vec4F avg(0.0f); for (uint32_t y = 0; y < src.get_height(); y++) { for (uint32_t x = 0; x < src.get_width(); x++) { const vec4F &s = src(x, y); avg += vec4F(s[0], s[1], s[2], s[3]); } } avg /= static_cast(src.get_total_pixels()); return avg; } // Reference: https://ece.uwaterloo.ca/~z70wang/research/ssim/index.html vec4F compute_ssim(const imagef &a, const imagef &b) { imagef axb, a_sq, b_sq, mu1, mu2, mu1_sq, mu2_sq, mu1_mu2, s1_sq, s2_sq, s12, smap, t1, t2, t3; const float C1 = 6.50250f, C2 = 58.52250f; pow_image(a, a_sq, vec4F(2)); pow_image(b, b_sq, vec4F(2)); mul_image(a, b, axb, vec4F(1.0f)); gaussian_filter(mu1, a, 11, 1.5f * 1.5f); gaussian_filter(mu2, b, 11, 1.5f * 1.5f); pow_image(mu1, mu1_sq, vec4F(2)); pow_image(mu2, mu2_sq, vec4F(2)); mul_image(mu1, mu2, mu1_mu2, vec4F(1.0f)); gaussian_filter(s1_sq, a_sq, 11, 1.5f * 1.5f); add_weighted_image(s1_sq, vec4F(1), mu1_sq, vec4F(-1), vec4F(0), s1_sq); gaussian_filter(s2_sq, b_sq, 11, 1.5f * 1.5f); add_weighted_image(s2_sq, vec4F(1), mu2_sq, vec4F(-1), vec4F(0), s2_sq); gaussian_filter(s12, axb, 11, 1.5f * 1.5f); add_weighted_image(s12, vec4F(1), mu1_mu2, vec4F(-1), vec4F(0), s12); scale_image(mu1_mu2, t1, vec4F(2), vec4F(0)); adds_image(t1, vec4F(C1), t1); scale_image(s12, t2, vec4F(2), vec4F(0)); adds_image(t2, vec4F(C2), t2); mul_image(t1, t2, t3, vec4F(1)); add_image(mu1_sq, mu2_sq, t1); adds_image(t1, vec4F(C1), t1); add_image(s1_sq, s2_sq, t2); adds_image(t2, vec4F(C2), t2); mul_image(t1, t2, t1, vec4F(1)); div_image(t3, t1, smap, vec4F(1)); return avg_image(smap); } vec4F compute_ssim(const image &a, const image &b, bool luma, bool luma_601) { image ta(a), tb(b); if ((ta.get_width() != tb.get_width()) || (ta.get_height() != tb.get_height())) { debug_printf("compute_ssim: Cropping input images to equal dimensions\n"); const uint32_t w = minimum(a.get_width(), b.get_width()); const uint32_t h = minimum(a.get_height(), b.get_height()); ta.crop(w, h); tb.crop(w, h); } if (!ta.get_width() || !ta.get_height()) { assert(0); return vec4F(0); } if (luma) { for (uint32_t y = 0; y < ta.get_height(); y++) { for (uint32_t x = 0; x < ta.get_width(); x++) { ta(x, y).set(ta(x, y).get_luma(luma_601), ta(x, y).a); tb(x, y).set(tb(x, y).get_luma(luma_601), tb(x, y).a); } } } imagef fta, ftb; fta.set(ta); ftb.set(tb); return compute_ssim(fta, ftb); } } // namespace basisu