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+/*
+ * Copyright (c) 2016, Alliance for Open Media. All rights reserved
+ *
+ * This source code is subject to the terms of the BSD 2 Clause License and
+ * the Alliance for Open Media Patent License 1.0. If the BSD 2 Clause License
+ * was not distributed with this source code in the LICENSE file, you can
+ * obtain it at www.aomedia.org/license/software. If the Alliance for Open
+ * Media Patent License 1.0 was not distributed with this source code in the
+ * PATENTS file, you can obtain it at www.aomedia.org/license/patent.
+ */
+
+#include <assert.h>
+#include <math.h>
+
+#include "config/aom_dsp_rtcd.h"
+
+#include "aom_dsp/ssim.h"
+#include "aom_ports/mem.h"
+#include "aom_ports/system_state.h"
+
+void aom_ssim_parms_16x16_c(const uint8_t *s, int sp, const uint8_t *r, int rp,
+ uint32_t *sum_s, uint32_t *sum_r,
+ uint32_t *sum_sq_s, uint32_t *sum_sq_r,
+ uint32_t *sum_sxr) {
+ int i, j;
+ for (i = 0; i < 16; i++, s += sp, r += rp) {
+ for (j = 0; j < 16; j++) {
+ *sum_s += s[j];
+ *sum_r += r[j];
+ *sum_sq_s += s[j] * s[j];
+ *sum_sq_r += r[j] * r[j];
+ *sum_sxr += s[j] * r[j];
+ }
+ }
+}
+
+void aom_ssim_parms_8x8_c(const uint8_t *s, int sp, const uint8_t *r, int rp,
+ uint32_t *sum_s, uint32_t *sum_r, uint32_t *sum_sq_s,
+ uint32_t *sum_sq_r, uint32_t *sum_sxr) {
+ int i, j;
+ for (i = 0; i < 8; i++, s += sp, r += rp) {
+ for (j = 0; j < 8; j++) {
+ *sum_s += s[j];
+ *sum_r += r[j];
+ *sum_sq_s += s[j] * s[j];
+ *sum_sq_r += r[j] * r[j];
+ *sum_sxr += s[j] * r[j];
+ }
+ }
+}
+
+void aom_highbd_ssim_parms_8x8_c(const uint16_t *s, int sp, const uint16_t *r,
+ int rp, uint32_t *sum_s, uint32_t *sum_r,
+ uint32_t *sum_sq_s, uint32_t *sum_sq_r,
+ uint32_t *sum_sxr) {
+ int i, j;
+ for (i = 0; i < 8; i++, s += sp, r += rp) {
+ for (j = 0; j < 8; j++) {
+ *sum_s += s[j];
+ *sum_r += r[j];
+ *sum_sq_s += s[j] * s[j];
+ *sum_sq_r += r[j] * r[j];
+ *sum_sxr += s[j] * r[j];
+ }
+ }
+}
+
+static const int64_t cc1 = 26634; // (64^2*(.01*255)^2
+static const int64_t cc2 = 239708; // (64^2*(.03*255)^2
+static const int64_t cc1_10 = 428658; // (64^2*(.01*1023)^2
+static const int64_t cc2_10 = 3857925; // (64^2*(.03*1023)^2
+static const int64_t cc1_12 = 6868593; // (64^2*(.01*4095)^2
+static const int64_t cc2_12 = 61817334; // (64^2*(.03*4095)^2
+
+static double similarity(uint32_t sum_s, uint32_t sum_r, uint32_t sum_sq_s,
+ uint32_t sum_sq_r, uint32_t sum_sxr, int count,
+ uint32_t bd) {
+ int64_t ssim_n, ssim_d;
+ int64_t c1, c2;
+ if (bd == 8) {
+ // scale the constants by number of pixels
+ c1 = (cc1 * count * count) >> 12;
+ c2 = (cc2 * count * count) >> 12;
+ } else if (bd == 10) {
+ c1 = (cc1_10 * count * count) >> 12;
+ c2 = (cc2_10 * count * count) >> 12;
+ } else if (bd == 12) {
+ c1 = (cc1_12 * count * count) >> 12;
+ c2 = (cc2_12 * count * count) >> 12;
+ } else {
+ c1 = c2 = 0;
+ assert(0);
+ }
+
+ ssim_n = (2 * sum_s * sum_r + c1) *
+ ((int64_t)2 * count * sum_sxr - (int64_t)2 * sum_s * sum_r + c2);
+
+ ssim_d = (sum_s * sum_s + sum_r * sum_r + c1) *
+ ((int64_t)count * sum_sq_s - (int64_t)sum_s * sum_s +
+ (int64_t)count * sum_sq_r - (int64_t)sum_r * sum_r + c2);
+
+ return ssim_n * 1.0 / ssim_d;
+}
+
+static double ssim_8x8(const uint8_t *s, int sp, const uint8_t *r, int rp) {
+ uint32_t sum_s = 0, sum_r = 0, sum_sq_s = 0, sum_sq_r = 0, sum_sxr = 0;
+ aom_ssim_parms_8x8(s, sp, r, rp, &sum_s, &sum_r, &sum_sq_s, &sum_sq_r,
+ &sum_sxr);
+ return similarity(sum_s, sum_r, sum_sq_s, sum_sq_r, sum_sxr, 64, 8);
+}
+
+static double highbd_ssim_8x8(const uint16_t *s, int sp, const uint16_t *r,
+ int rp, uint32_t bd, uint32_t shift) {
+ uint32_t sum_s = 0, sum_r = 0, sum_sq_s = 0, sum_sq_r = 0, sum_sxr = 0;
+ aom_highbd_ssim_parms_8x8(s, sp, r, rp, &sum_s, &sum_r, &sum_sq_s, &sum_sq_r,
+ &sum_sxr);
+ return similarity(sum_s >> shift, sum_r >> shift, sum_sq_s >> (2 * shift),
+ sum_sq_r >> (2 * shift), sum_sxr >> (2 * shift), 64, bd);
+}
+
+// We are using a 8x8 moving window with starting location of each 8x8 window
+// on the 4x4 pixel grid. Such arrangement allows the windows to overlap
+// block boundaries to penalize blocking artifacts.
+static double aom_ssim2(const uint8_t *img1, const uint8_t *img2,
+ int stride_img1, int stride_img2, int width,
+ int height) {
+ int i, j;
+ int samples = 0;
+ double ssim_total = 0;
+
+ // sample point start with each 4x4 location
+ for (i = 0; i <= height - 8;
+ i += 4, img1 += stride_img1 * 4, img2 += stride_img2 * 4) {
+ for (j = 0; j <= width - 8; j += 4) {
+ double v = ssim_8x8(img1 + j, stride_img1, img2 + j, stride_img2);
+ ssim_total += v;
+ samples++;
+ }
+ }
+ ssim_total /= samples;
+ return ssim_total;
+}
+
+static double aom_highbd_ssim2(const uint8_t *img1, const uint8_t *img2,
+ int stride_img1, int stride_img2, int width,
+ int height, uint32_t bd, uint32_t shift) {
+ int i, j;
+ int samples = 0;
+ double ssim_total = 0;
+
+ // sample point start with each 4x4 location
+ for (i = 0; i <= height - 8;
+ i += 4, img1 += stride_img1 * 4, img2 += stride_img2 * 4) {
+ for (j = 0; j <= width - 8; j += 4) {
+ double v = highbd_ssim_8x8(CONVERT_TO_SHORTPTR(img1 + j), stride_img1,
+ CONVERT_TO_SHORTPTR(img2 + j), stride_img2, bd,
+ shift);
+ ssim_total += v;
+ samples++;
+ }
+ }
+ ssim_total /= samples;
+ return ssim_total;
+}
+
+double aom_calc_ssim(const YV12_BUFFER_CONFIG *source,
+ const YV12_BUFFER_CONFIG *dest, double *weight) {
+ double abc[3];
+ for (int i = 0; i < 3; ++i) {
+ const int is_uv = i > 0;
+ abc[i] = aom_ssim2(source->buffers[i], dest->buffers[i],
+ source->strides[is_uv], dest->strides[is_uv],
+ source->crop_widths[is_uv], source->crop_heights[is_uv]);
+ }
+
+ *weight = 1;
+ return abc[0] * .8 + .1 * (abc[1] + abc[2]);
+}
+
+// traditional ssim as per: http://en.wikipedia.org/wiki/Structural_similarity
+//
+// Re working out the math ->
+//
+// ssim(x,y) = (2*mean(x)*mean(y) + c1)*(2*cov(x,y)+c2) /
+// ((mean(x)^2+mean(y)^2+c1)*(var(x)+var(y)+c2))
+//
+// mean(x) = sum(x) / n
+//
+// cov(x,y) = (n*sum(xi*yi)-sum(x)*sum(y))/(n*n)
+//
+// var(x) = (n*sum(xi*xi)-sum(xi)*sum(xi))/(n*n)
+//
+// ssim(x,y) =
+// (2*sum(x)*sum(y)/(n*n) + c1)*(2*(n*sum(xi*yi)-sum(x)*sum(y))/(n*n)+c2) /
+// (((sum(x)*sum(x)+sum(y)*sum(y))/(n*n) +c1) *
+// ((n*sum(xi*xi) - sum(xi)*sum(xi))/(n*n)+
+// (n*sum(yi*yi) - sum(yi)*sum(yi))/(n*n)+c2)))
+//
+// factoring out n*n
+//
+// ssim(x,y) =
+// (2*sum(x)*sum(y) + n*n*c1)*(2*(n*sum(xi*yi)-sum(x)*sum(y))+n*n*c2) /
+// (((sum(x)*sum(x)+sum(y)*sum(y)) + n*n*c1) *
+// (n*sum(xi*xi)-sum(xi)*sum(xi)+n*sum(yi*yi)-sum(yi)*sum(yi)+n*n*c2))
+//
+// Replace c1 with n*n * c1 for the final step that leads to this code:
+// The final step scales by 12 bits so we don't lose precision in the constants.
+
+static double ssimv_similarity(const Ssimv *sv, int64_t n) {
+ // Scale the constants by number of pixels.
+ const int64_t c1 = (cc1 * n * n) >> 12;
+ const int64_t c2 = (cc2 * n * n) >> 12;
+
+ const double l = 1.0 * (2 * sv->sum_s * sv->sum_r + c1) /
+ (sv->sum_s * sv->sum_s + sv->sum_r * sv->sum_r + c1);
+
+ // Since these variables are unsigned sums, convert to double so
+ // math is done in double arithmetic.
+ const double v = (2.0 * n * sv->sum_sxr - 2 * sv->sum_s * sv->sum_r + c2) /
+ (n * sv->sum_sq_s - sv->sum_s * sv->sum_s +
+ n * sv->sum_sq_r - sv->sum_r * sv->sum_r + c2);
+
+ return l * v;
+}
+
+// The first term of the ssim metric is a luminance factor.
+//
+// (2*mean(x)*mean(y) + c1)/ (mean(x)^2+mean(y)^2+c1)
+//
+// This luminance factor is super sensitive to the dark side of luminance
+// values and completely insensitive on the white side. check out 2 sets
+// (1,3) and (250,252) the term gives ( 2*1*3/(1+9) = .60
+// 2*250*252/ (250^2+252^2) => .99999997
+//
+// As a result in this tweaked version of the calculation in which the
+// luminance is taken as percentage off from peak possible.
+//
+// 255 * 255 - (sum_s - sum_r) / count * (sum_s - sum_r) / count
+//
+static double ssimv_similarity2(const Ssimv *sv, int64_t n) {
+ // Scale the constants by number of pixels.
+ const int64_t c1 = (cc1 * n * n) >> 12;
+ const int64_t c2 = (cc2 * n * n) >> 12;
+
+ const double mean_diff = (1.0 * sv->sum_s - sv->sum_r) / n;
+ const double l = (255 * 255 - mean_diff * mean_diff + c1) / (255 * 255 + c1);
+
+ // Since these variables are unsigned, sums convert to double so
+ // math is done in double arithmetic.
+ const double v = (2.0 * n * sv->sum_sxr - 2 * sv->sum_s * sv->sum_r + c2) /
+ (n * sv->sum_sq_s - sv->sum_s * sv->sum_s +
+ n * sv->sum_sq_r - sv->sum_r * sv->sum_r + c2);
+
+ return l * v;
+}
+static void ssimv_parms(uint8_t *img1, int img1_pitch, uint8_t *img2,
+ int img2_pitch, Ssimv *sv) {
+ aom_ssim_parms_8x8(img1, img1_pitch, img2, img2_pitch, &sv->sum_s, &sv->sum_r,
+ &sv->sum_sq_s, &sv->sum_sq_r, &sv->sum_sxr);
+}
+
+double aom_get_ssim_metrics(uint8_t *img1, int img1_pitch, uint8_t *img2,
+ int img2_pitch, int width, int height, Ssimv *sv2,
+ Metrics *m, int do_inconsistency) {
+ double dssim_total = 0;
+ double ssim_total = 0;
+ double ssim2_total = 0;
+ double inconsistency_total = 0;
+ int i, j;
+ int c = 0;
+ double norm;
+ double old_ssim_total = 0;
+ aom_clear_system_state();
+ // We can sample points as frequently as we like start with 1 per 4x4.
+ for (i = 0; i < height;
+ i += 4, img1 += img1_pitch * 4, img2 += img2_pitch * 4) {
+ for (j = 0; j < width; j += 4, ++c) {
+ Ssimv sv = { 0, 0, 0, 0, 0, 0 };
+ double ssim;
+ double ssim2;
+ double dssim;
+ uint32_t var_new;
+ uint32_t var_old;
+ uint32_t mean_new;
+ uint32_t mean_old;
+ double ssim_new;
+ double ssim_old;
+
+ // Not sure there's a great way to handle the edge pixels
+ // in ssim when using a window. Seems biased against edge pixels
+ // however you handle this. This uses only samples that are
+ // fully in the frame.
+ if (j + 8 <= width && i + 8 <= height) {
+ ssimv_parms(img1 + j, img1_pitch, img2 + j, img2_pitch, &sv);
+ }
+
+ ssim = ssimv_similarity(&sv, 64);
+ ssim2 = ssimv_similarity2(&sv, 64);
+
+ sv.ssim = ssim2;
+
+ // dssim is calculated to use as an actual error metric and
+ // is scaled up to the same range as sum square error.
+ // Since we are subsampling every 16th point maybe this should be
+ // *16 ?
+ dssim = 255 * 255 * (1 - ssim2) / 2;
+
+ // Here I introduce a new error metric: consistency-weighted
+ // SSIM-inconsistency. This metric isolates frames where the
+ // SSIM 'suddenly' changes, e.g. if one frame in every 8 is much
+ // sharper or blurrier than the others. Higher values indicate a
+ // temporally inconsistent SSIM. There are two ideas at work:
+ //
+ // 1) 'SSIM-inconsistency': the total inconsistency value
+ // reflects how much SSIM values are changing between this
+ // source / reference frame pair and the previous pair.
+ //
+ // 2) 'consistency-weighted': weights de-emphasize areas in the
+ // frame where the scene content has changed. Changes in scene
+ // content are detected via changes in local variance and local
+ // mean.
+ //
+ // Thus the overall measure reflects how inconsistent the SSIM
+ // values are, over consistent regions of the frame.
+ //
+ // The metric has three terms:
+ //
+ // term 1 -> uses change in scene Variance to weight error score
+ // 2 * var(Fi)*var(Fi-1) / (var(Fi)^2+var(Fi-1)^2)
+ // larger changes from one frame to the next mean we care
+ // less about consistency.
+ //
+ // term 2 -> uses change in local scene luminance to weight error
+ // 2 * avg(Fi)*avg(Fi-1) / (avg(Fi)^2+avg(Fi-1)^2)
+ // larger changes from one frame to the next mean we care
+ // less about consistency.
+ //
+ // term3 -> measures inconsistency in ssim scores between frames
+ // 1 - ( 2 * ssim(Fi)*ssim(Fi-1)/(ssim(Fi)^2+sssim(Fi-1)^2).
+ //
+ // This term compares the ssim score for the same location in 2
+ // subsequent frames.
+ var_new = sv.sum_sq_s - sv.sum_s * sv.sum_s / 64;
+ var_old = sv2[c].sum_sq_s - sv2[c].sum_s * sv2[c].sum_s / 64;
+ mean_new = sv.sum_s;
+ mean_old = sv2[c].sum_s;
+ ssim_new = sv.ssim;
+ ssim_old = sv2[c].ssim;
+
+ if (do_inconsistency) {
+ // We do the metric once for every 4x4 block in the image. Since
+ // we are scaling the error to SSE for use in a psnr calculation
+ // 1.0 = 4x4x255x255 the worst error we can possibly have.
+ static const double kScaling = 4. * 4 * 255 * 255;
+
+ // The constants have to be non 0 to avoid potential divide by 0
+ // issues other than that they affect kind of a weighting between
+ // the terms. No testing of what the right terms should be has been
+ // done.
+ static const double c1 = 1, c2 = 1, c3 = 1;
+
+ // This measures how much consistent variance is in two consecutive
+ // source frames. 1.0 means they have exactly the same variance.
+ const double variance_term =
+ (2.0 * var_old * var_new + c1) /
+ (1.0 * var_old * var_old + 1.0 * var_new * var_new + c1);
+
+ // This measures how consistent the local mean are between two
+ // consecutive frames. 1.0 means they have exactly the same mean.
+ const double mean_term =
+ (2.0 * mean_old * mean_new + c2) /
+ (1.0 * mean_old * mean_old + 1.0 * mean_new * mean_new + c2);
+
+ // This measures how consistent the ssims of two
+ // consecutive frames is. 1.0 means they are exactly the same.
+ double ssim_term =
+ pow((2.0 * ssim_old * ssim_new + c3) /
+ (ssim_old * ssim_old + ssim_new * ssim_new + c3),
+ 5);
+
+ double this_inconsistency;
+
+ // Floating point math sometimes makes this > 1 by a tiny bit.
+ // We want the metric to scale between 0 and 1.0 so we can convert
+ // it to an snr scaled value.
+ if (ssim_term > 1) ssim_term = 1;
+
+ // This converts the consistency metric to an inconsistency metric
+ // ( so we can scale it like psnr to something like sum square error.
+ // The reason for the variance and mean terms is the assumption that
+ // if there are big changes in the source we shouldn't penalize
+ // inconsistency in ssim scores a bit less as it will be less visible
+ // to the user.
+ this_inconsistency = (1 - ssim_term) * variance_term * mean_term;
+
+ this_inconsistency *= kScaling;
+ inconsistency_total += this_inconsistency;
+ }
+ sv2[c] = sv;
+ ssim_total += ssim;
+ ssim2_total += ssim2;
+ dssim_total += dssim;
+
+ old_ssim_total += ssim_old;
+ }
+ old_ssim_total += 0;
+ }
+
+ norm = 1. / (width / 4) / (height / 4);
+ ssim_total *= norm;
+ ssim2_total *= norm;
+ m->ssim2 = ssim2_total;
+ m->ssim = ssim_total;
+ if (old_ssim_total == 0) inconsistency_total = 0;
+
+ m->ssimc = inconsistency_total;
+
+ m->dssim = dssim_total;
+ return inconsistency_total;
+}
+
+double aom_highbd_calc_ssim(const YV12_BUFFER_CONFIG *source,
+ const YV12_BUFFER_CONFIG *dest, double *weight,
+ uint32_t bd, uint32_t in_bd) {
+ assert(bd >= in_bd);
+ const uint32_t shift = bd - in_bd;
+
+ double abc[3];
+ for (int i = 0; i < 3; ++i) {
+ const int is_uv = i > 0;
+ abc[i] = aom_highbd_ssim2(source->buffers[i], dest->buffers[i],
+ source->strides[is_uv], dest->strides[is_uv],
+ source->crop_widths[is_uv],
+ source->crop_heights[is_uv], in_bd, shift);
+ }
+
+ *weight = 1;
+ return abc[0] * .8 + .1 * (abc[1] + abc[2]);
+}
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