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+/*
+ * Copyright 2013 The LibYuv 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 "../util/ssim.h" // NOLINT
+
+#include <string.h>
+
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+typedef unsigned int uint32; // NOLINT
+typedef unsigned short uint16; // NOLINT
+
+#if !defined(LIBYUV_DISABLE_X86) && !defined(__SSE2__) && \
+ (defined(_M_X64) || (defined(_M_IX86_FP) && (_M_IX86_FP >= 2)))
+#define __SSE2__
+#endif
+#if !defined(LIBYUV_DISABLE_X86) && defined(__SSE2__)
+#include <emmintrin.h>
+#endif
+
+#ifdef _OPENMP
+#include <omp.h>
+#endif
+
+// SSIM
+enum { KERNEL = 3, KERNEL_SIZE = 2 * KERNEL + 1 };
+
+// Symmetric Gaussian kernel: K[i] = ~11 * exp(-0.3 * i * i)
+// The maximum value (11 x 11) must be less than 128 to avoid sign
+// problems during the calls to _mm_mullo_epi16().
+static const int K[KERNEL_SIZE] = {
+ 1, 3, 7, 11, 7, 3, 1 // ~11 * exp(-0.3 * i * i)
+};
+static const double kiW[KERNEL + 1 + 1] = {
+ 1. / 1089., // 1 / sum(i:0..6, j..6) K[i]*K[j]
+ 1. / 1089., // 1 / sum(i:0..6, j..6) K[i]*K[j]
+ 1. / 1056., // 1 / sum(i:0..5, j..6) K[i]*K[j]
+ 1. / 957., // 1 / sum(i:0..4, j..6) K[i]*K[j]
+ 1. / 726., // 1 / sum(i:0..3, j..6) K[i]*K[j]
+};
+
+#if !defined(LIBYUV_DISABLE_X86) && defined(__SSE2__)
+
+#define PWEIGHT(A, B) static_cast<uint16>(K[(A)] * K[(B)]) // weight product
+#define MAKE_WEIGHT(L) \
+ { { { PWEIGHT(L, 0), PWEIGHT(L, 1), PWEIGHT(L, 2), PWEIGHT(L, 3), \
+ PWEIGHT(L, 4), PWEIGHT(L, 5), PWEIGHT(L, 6), 0 } } }
+
+// We need this union trick to be able to initialize constant static __m128i
+// values. We can't call _mm_set_epi16() for static compile-time initialization.
+static const struct {
+ union {
+ uint16 i16_[8];
+ __m128i m_;
+ } values_;
+} W0 = MAKE_WEIGHT(0),
+ W1 = MAKE_WEIGHT(1),
+ W2 = MAKE_WEIGHT(2),
+ W3 = MAKE_WEIGHT(3);
+ // ... the rest is symmetric.
+#undef MAKE_WEIGHT
+#undef PWEIGHT
+#endif
+
+// Common final expression for SSIM, once the weighted sums are known.
+static double FinalizeSSIM(double iw, double xm, double ym,
+ double xxm, double xym, double yym) {
+ const double iwx = xm * iw;
+ const double iwy = ym * iw;
+ double sxx = xxm * iw - iwx * iwx;
+ double syy = yym * iw - iwy * iwy;
+ // small errors are possible, due to rounding. Clamp to zero.
+ if (sxx < 0.) sxx = 0.;
+ if (syy < 0.) syy = 0.;
+ const double sxsy = sqrt(sxx * syy);
+ const double sxy = xym * iw - iwx * iwy;
+ static const double C11 = (0.01 * 0.01) * (255 * 255);
+ static const double C22 = (0.03 * 0.03) * (255 * 255);
+ static const double C33 = (0.015 * 0.015) * (255 * 255);
+ const double l = (2. * iwx * iwy + C11) / (iwx * iwx + iwy * iwy + C11);
+ const double c = (2. * sxsy + C22) / (sxx + syy + C22);
+ const double s = (sxy + C33) / (sxsy + C33);
+ return l * c * s;
+}
+
+// GetSSIM() does clipping. GetSSIMFullKernel() does not
+
+// TODO(skal): use summed tables?
+// Note: worst case of accumulation is a weight of 33 = 11 + 2 * (7 + 3 + 1)
+// with a diff of 255, squared. The maximum error is thus 0x4388241,
+// which fits into 32 bits integers.
+double GetSSIM(const uint8 *org, const uint8 *rec,
+ int xo, int yo, int W, int H, int stride) {
+ uint32 ws = 0, xm = 0, ym = 0, xxm = 0, xym = 0, yym = 0;
+ org += (yo - KERNEL) * stride;
+ org += (xo - KERNEL);
+ rec += (yo - KERNEL) * stride;
+ rec += (xo - KERNEL);
+ for (int y_ = 0; y_ < KERNEL_SIZE; ++y_, org += stride, rec += stride) {
+ if (((yo - KERNEL + y_) < 0) || ((yo - KERNEL + y_) >= H)) continue;
+ const int Wy = K[y_];
+ for (int x_ = 0; x_ < KERNEL_SIZE; ++x_) {
+ const int Wxy = Wy * K[x_];
+ if (((xo - KERNEL + x_) >= 0) && ((xo - KERNEL + x_) < W)) {
+ const int org_x = org[x_];
+ const int rec_x = rec[x_];
+ ws += Wxy;
+ xm += Wxy * org_x;
+ ym += Wxy * rec_x;
+ xxm += Wxy * org_x * org_x;
+ xym += Wxy * org_x * rec_x;
+ yym += Wxy * rec_x * rec_x;
+ }
+ }
+ }
+ return FinalizeSSIM(1. / ws, xm, ym, xxm, xym, yym);
+}
+
+double GetSSIMFullKernel(const uint8 *org, const uint8 *rec,
+ int xo, int yo, int stride,
+ double area_weight) {
+ uint32 xm = 0, ym = 0, xxm = 0, xym = 0, yym = 0;
+
+#if defined(LIBYUV_DISABLE_X86) || !defined(__SSE2__)
+
+ org += yo * stride + xo;
+ rec += yo * stride + xo;
+ for (int y = 1; y <= KERNEL; y++) {
+ const int dy1 = y * stride;
+ const int dy2 = y * stride;
+ const int Wy = K[KERNEL + y];
+
+ for (int x = 1; x <= KERNEL; x++) {
+ // Compute the contributions of upper-left (ul), upper-right (ur)
+ // lower-left (ll) and lower-right (lr) points (see the diagram below).
+ // Symmetric Kernel will have same weight on those points.
+ // - - - - - - -
+ // - ul - - - ur -
+ // - - - - - - -
+ // - - - 0 - - -
+ // - - - - - - -
+ // - ll - - - lr -
+ // - - - - - - -
+ const int Wxy = Wy * K[KERNEL + x];
+ const int ul1 = org[-dy1 - x];
+ const int ur1 = org[-dy1 + x];
+ const int ll1 = org[dy1 - x];
+ const int lr1 = org[dy1 + x];
+
+ const int ul2 = rec[-dy2 - x];
+ const int ur2 = rec[-dy2 + x];
+ const int ll2 = rec[dy2 - x];
+ const int lr2 = rec[dy2 + x];
+
+ xm += Wxy * (ul1 + ur1 + ll1 + lr1);
+ ym += Wxy * (ul2 + ur2 + ll2 + lr2);
+ xxm += Wxy * (ul1 * ul1 + ur1 * ur1 + ll1 * ll1 + lr1 * lr1);
+ xym += Wxy * (ul1 * ul2 + ur1 * ur2 + ll1 * ll2 + lr1 * lr2);
+ yym += Wxy * (ul2 * ul2 + ur2 * ur2 + ll2 * ll2 + lr2 * lr2);
+ }
+
+ // Compute the contributions of up (u), down (d), left (l) and right (r)
+ // points across the main axes (see the diagram below).
+ // Symmetric Kernel will have same weight on those points.
+ // - - - - - - -
+ // - - - u - - -
+ // - - - - - - -
+ // - l - 0 - r -
+ // - - - - - - -
+ // - - - d - - -
+ // - - - - - - -
+ const int Wxy = Wy * K[KERNEL];
+ const int u1 = org[-dy1];
+ const int d1 = org[dy1];
+ const int l1 = org[-y];
+ const int r1 = org[y];
+
+ const int u2 = rec[-dy2];
+ const int d2 = rec[dy2];
+ const int l2 = rec[-y];
+ const int r2 = rec[y];
+
+ xm += Wxy * (u1 + d1 + l1 + r1);
+ ym += Wxy * (u2 + d2 + l2 + r2);
+ xxm += Wxy * (u1 * u1 + d1 * d1 + l1 * l1 + r1 * r1);
+ xym += Wxy * (u1 * u2 + d1 * d2 + l1 * l2 + r1 * r2);
+ yym += Wxy * (u2 * u2 + d2 * d2 + l2 * l2 + r2 * r2);
+ }
+
+ // Lastly the contribution of (x0, y0) point.
+ const int Wxy = K[KERNEL] * K[KERNEL];
+ const int s1 = org[0];
+ const int s2 = rec[0];
+
+ xm += Wxy * s1;
+ ym += Wxy * s2;
+ xxm += Wxy * s1 * s1;
+ xym += Wxy * s1 * s2;
+ yym += Wxy * s2 * s2;
+
+#else // __SSE2__
+
+ org += (yo - KERNEL) * stride + (xo - KERNEL);
+ rec += (yo - KERNEL) * stride + (xo - KERNEL);
+
+ const __m128i zero = _mm_setzero_si128();
+ __m128i x = zero;
+ __m128i y = zero;
+ __m128i xx = zero;
+ __m128i xy = zero;
+ __m128i yy = zero;
+
+// Read 8 pixels at line #L, and convert to 16bit, perform weighting
+// and acccumulate.
+#define LOAD_LINE_PAIR(L, WEIGHT) do { \
+ const __m128i v0 = \
+ _mm_loadl_epi64(reinterpret_cast<const __m128i*>(org + (L) * stride)); \
+ const __m128i v1 = \
+ _mm_loadl_epi64(reinterpret_cast<const __m128i*>(rec + (L) * stride)); \
+ const __m128i w0 = _mm_unpacklo_epi8(v0, zero); \
+ const __m128i w1 = _mm_unpacklo_epi8(v1, zero); \
+ const __m128i ww0 = _mm_mullo_epi16(w0, (WEIGHT).values_.m_); \
+ const __m128i ww1 = _mm_mullo_epi16(w1, (WEIGHT).values_.m_); \
+ x = _mm_add_epi32(x, _mm_unpacklo_epi16(ww0, zero)); \
+ y = _mm_add_epi32(y, _mm_unpacklo_epi16(ww1, zero)); \
+ x = _mm_add_epi32(x, _mm_unpackhi_epi16(ww0, zero)); \
+ y = _mm_add_epi32(y, _mm_unpackhi_epi16(ww1, zero)); \
+ xx = _mm_add_epi32(xx, _mm_madd_epi16(ww0, w0)); \
+ xy = _mm_add_epi32(xy, _mm_madd_epi16(ww0, w1)); \
+ yy = _mm_add_epi32(yy, _mm_madd_epi16(ww1, w1)); \
+} while (0)
+
+#define ADD_AND_STORE_FOUR_EPI32(M, OUT) do { \
+ uint32 tmp[4]; \
+ _mm_storeu_si128(reinterpret_cast<__m128i*>(tmp), (M)); \
+ (OUT) = tmp[3] + tmp[2] + tmp[1] + tmp[0]; \
+} while (0)
+
+ LOAD_LINE_PAIR(0, W0);
+ LOAD_LINE_PAIR(1, W1);
+ LOAD_LINE_PAIR(2, W2);
+ LOAD_LINE_PAIR(3, W3);
+ LOAD_LINE_PAIR(4, W2);
+ LOAD_LINE_PAIR(5, W1);
+ LOAD_LINE_PAIR(6, W0);
+
+ ADD_AND_STORE_FOUR_EPI32(x, xm);
+ ADD_AND_STORE_FOUR_EPI32(y, ym);
+ ADD_AND_STORE_FOUR_EPI32(xx, xxm);
+ ADD_AND_STORE_FOUR_EPI32(xy, xym);
+ ADD_AND_STORE_FOUR_EPI32(yy, yym);
+
+#undef LOAD_LINE_PAIR
+#undef ADD_AND_STORE_FOUR_EPI32
+#endif
+
+ return FinalizeSSIM(area_weight, xm, ym, xxm, xym, yym);
+}
+
+static int start_max(int x, int y) { return (x > y) ? x : y; }
+
+double CalcSSIM(const uint8 *org, const uint8 *rec,
+ const int image_width, const int image_height) {
+ double SSIM = 0.;
+ const int KERNEL_Y = (image_height < KERNEL) ? image_height : KERNEL;
+ const int KERNEL_X = (image_width < KERNEL) ? image_width : KERNEL;
+ const int start_x = start_max(image_width - 8 + KERNEL_X, KERNEL_X);
+ const int start_y = start_max(image_height - KERNEL_Y, KERNEL_Y);
+ const int stride = image_width;
+
+ for (int j = 0; j < KERNEL_Y; ++j) {
+ for (int i = 0; i < image_width; ++i) {
+ SSIM += GetSSIM(org, rec, i, j, image_width, image_height, stride);
+ }
+ }
+
+#ifdef _OPENMP
+ #pragma omp parallel for reduction(+: SSIM)
+#endif
+ for (int j = KERNEL_Y; j < image_height - KERNEL_Y; ++j) {
+ for (int i = 0; i < KERNEL_X; ++i) {
+ SSIM += GetSSIM(org, rec, i, j, image_width, image_height, stride);
+ }
+ for (int i = KERNEL_X; i < start_x; ++i) {
+ SSIM += GetSSIMFullKernel(org, rec, i, j, stride, kiW[0]);
+ }
+ if (start_x < image_width) {
+ // GetSSIMFullKernel() needs to be able to read 8 pixels (in SSE2). So we
+ // copy the 8 rightmost pixels on a cache area, and pad this area with
+ // zeros which won't contribute to the overall SSIM value (but we need
+ // to pass the correct normalizing constant!). By using this cache, we can
+ // still call GetSSIMFullKernel() instead of the slower GetSSIM().
+ // NOTE: we could use similar method for the left-most pixels too.
+ const int kScratchWidth = 8;
+ const int kScratchStride = kScratchWidth + KERNEL + 1;
+ uint8 scratch_org[KERNEL_SIZE * kScratchStride] = { 0 };
+ uint8 scratch_rec[KERNEL_SIZE * kScratchStride] = { 0 };
+
+ for (int k = 0; k < KERNEL_SIZE; ++k) {
+ const int offset =
+ (j - KERNEL + k) * stride + image_width - kScratchWidth;
+ memcpy(scratch_org + k * kScratchStride, org + offset, kScratchWidth);
+ memcpy(scratch_rec + k * kScratchStride, rec + offset, kScratchWidth);
+ }
+ for (int k = 0; k <= KERNEL_X + 1; ++k) {
+ SSIM += GetSSIMFullKernel(scratch_org, scratch_rec,
+ KERNEL + k, KERNEL, kScratchStride, kiW[k]);
+ }
+ }
+ }
+
+ for (int j = start_y; j < image_height; ++j) {
+ for (int i = 0; i < image_width; ++i) {
+ SSIM += GetSSIM(org, rec, i, j, image_width, image_height, stride);
+ }
+ }
+ return SSIM;
+}
+
+double CalcLSSIM(double ssim) {
+ return -10.0 * log10(1.0 - ssim);
+}
+
+#ifdef __cplusplus
+} // extern "C"
+#endif
+
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