ref: fc5ab625b5f8daa7f9f10667ca022fd404a71f61
dir: libvpx/vpx_dsp/ssim.c
/*
* Copyright (c) 2010 The WebM project authors. All Rights Reserved.
*
* Use of this source code is governed by a BSD-style license
* that can be found in the LICENSE file in the root of the source
* tree. An additional intellectual property rights grant can be found
* in the file PATENTS. All contributing project authors may
* be found in the AUTHORS file in the root of the source tree.
*/
#include <assert.h>
#include <math.h>
#include "./vpx_dsp_rtcd.h"
#include "vpx_dsp/ssim.h"
#include "vpx_ports/mem.h"
#include "vpx_ports/system_state.h"
void vpx_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 vpx_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];
}
}
}
#if CONFIG_VP9_HIGHBITDEPTH
void vpx_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];
}
}
}
#endif // CONFIG_VP9_HIGHBITDEPTH
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) {
double 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 = (2.0 * sum_s * sum_r + c1) *
(2.0 * count * sum_sxr - 2.0 * sum_s * sum_r + c2);
ssim_d = ((double)sum_s * sum_s + (double)sum_r * sum_r + c1) *
((double)count * sum_sq_s - (double)sum_s * sum_s +
(double)count * sum_sq_r - (double)sum_r * sum_r + c2);
return ssim_n / 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;
vpx_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);
}
#if CONFIG_VP9_HIGHBITDEPTH
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;
vpx_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);
}
#endif // CONFIG_VP9_HIGHBITDEPTH
// 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 vpx_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;
}
#if CONFIG_VP9_HIGHBITDEPTH
static double vpx_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;
}
#endif // CONFIG_VP9_HIGHBITDEPTH
double vpx_calc_ssim(const YV12_BUFFER_CONFIG *source,
const YV12_BUFFER_CONFIG *dest, double *weight) {
double a, b, c;
double ssimv;
a = vpx_ssim2(source->y_buffer, dest->y_buffer, source->y_stride,
dest->y_stride, source->y_crop_width, source->y_crop_height);
b = vpx_ssim2(source->u_buffer, dest->u_buffer, source->uv_stride,
dest->uv_stride, source->uv_crop_width, source->uv_crop_height);
c = vpx_ssim2(source->v_buffer, dest->v_buffer, source->uv_stride,
dest->uv_stride, source->uv_crop_width, source->uv_crop_height);
ssimv = a * .8 + .1 * (b + c);
*weight = 1;
return ssimv;
}
// 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) {
vpx_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 vpx_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;
vpx_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;
}
#if CONFIG_VP9_HIGHBITDEPTH
double vpx_highbd_calc_ssim(const YV12_BUFFER_CONFIG *source,
const YV12_BUFFER_CONFIG *dest, double *weight,
uint32_t bd, uint32_t in_bd) {
double a, b, c;
double ssimv;
uint32_t shift = 0;
assert(bd >= in_bd);
shift = bd - in_bd;
a = vpx_highbd_ssim2(source->y_buffer, dest->y_buffer, source->y_stride,
dest->y_stride, source->y_crop_width,
source->y_crop_height, in_bd, shift);
b = vpx_highbd_ssim2(source->u_buffer, dest->u_buffer, source->uv_stride,
dest->uv_stride, source->uv_crop_width,
source->uv_crop_height, in_bd, shift);
c = vpx_highbd_ssim2(source->v_buffer, dest->v_buffer, source->uv_stride,
dest->uv_stride, source->uv_crop_width,
source->uv_crop_height, in_bd, shift);
ssimv = a * .8 + .1 * (b + c);
*weight = 1;
return ssimv;
}
#endif // CONFIG_VP9_HIGHBITDEPTH