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+/*
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+ * Copyright (c) 2011, Tom Distler (http://tdistler.com)
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+ * All rights reserved.
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+ *
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+ * The BSD License
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+ *
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+ * Redistribution and use in source and binary forms, with or without
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+ * modification, are permitted provided that the following conditions are met:
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+ *
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+ * - Redistributions of source code must retain the above copyright notice,
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+ * this list of conditions and the following disclaimer.
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+ *
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+ * - Redistributions in binary form must reproduce the above copyright notice,
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+ * this list of conditions and the following disclaimer in the documentation
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+ * and/or other materials provided with the distribution.
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+ *
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+ * - Neither the name of the tdistler.com nor the names of its contributors may
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+ * be used to endorse or promote products derived from this software without
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+ * specific prior written permission.
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+ *
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+ * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
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+ * AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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+ * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
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+ * ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE
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+ * LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
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+ * CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
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+ * SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
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+ * INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
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+ * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
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+ * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
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+ * POSSIBILITY OF SUCH DAMAGE.
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+ */
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+
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+#include "iqa.h"
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+#include "convolve.h"
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+#include "decimate.h"
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+#include "math_utils.h"
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+#include "ssim.h"
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+#include <stdlib.h>
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+#include <math.h>
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+
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+
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+/* Forward declarations. */
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+IQA_INLINE static double _calc_luminance(float, float, float, float);
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+IQA_INLINE static double _calc_contrast(double, float, float, float, float);
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+IQA_INLINE static double _calc_structure(float, double, float, float, float, float);
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+static int _ssim_map(const struct _ssim_int *, void *);
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+static float _ssim_reduce(int, int, void *);
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+
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+/*
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+ * SSIM(x,y)=(2*ux*uy + C1)*(2sxy + C2) / (ux^2 + uy^2 + C1)*(sx^2 + sy^2 + C2)
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+ * where,
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+ * ux = SUM(w*x)
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+ * sx = (SUM(w*(x-ux)^2)^0.5
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+ * sxy = SUM(w*(x-ux)*(y-uy))
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+ *
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+ * Returns mean SSIM. MSSIM(X,Y) = 1/M * SUM(SSIM(x,y))
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+ */
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+float iqa_ssim(const unsigned char *ref, const unsigned char *cmp, int w, int h, int stride,
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+ int gaussian, const struct iqa_ssim_args *args)
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+{
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+ int scale;
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+ int x,y,src_offset,offset;
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+ float *ref_f,*cmp_f;
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+ struct _kernel low_pass;
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+ struct _kernel window;
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+ float result;
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+ double ssim_sum=0.0;
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+ struct _map_reduce mr;
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+
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+ /* Initialize algorithm parameters */
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+ scale = _max( 1, _round( (float)_min(w,h) / 256.0f ) );
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+ if (args) {
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+ if(args->f)
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+ scale = args->f;
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+ mr.map = _ssim_map;
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+ mr.reduce = _ssim_reduce;
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+ mr.context = (void*)&ssim_sum;
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+ }
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+ window.kernel = (float*)g_square_window;
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+ window.w = window.h = SQUARE_LEN;
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+ window.normalized = 1;
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+ window.bnd_opt = KBND_SYMMETRIC;
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+ if (gaussian) {
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+ window.kernel = (float*)g_gaussian_window;
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+ window.w = window.h = GAUSSIAN_LEN;
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+ }
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+
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+ /* Convert image values to floats. Forcing stride = width. */
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+ ref_f = (float*)malloc(w*h*sizeof(float));
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+ cmp_f = (float*)malloc(w*h*sizeof(float));
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+ if (!ref_f || !cmp_f) {
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+ if (ref_f) free(ref_f);
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+ if (cmp_f) free(cmp_f);
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+ return INFINITY;
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+ }
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+ for (y=0; y<h; ++y) {
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+ src_offset = y*stride;
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+ offset = y*w;
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+ for (x=0; x<w; ++x, ++offset, ++src_offset) {
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+ ref_f[offset] = (float)ref[src_offset];
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+ cmp_f[offset] = (float)cmp[src_offset];
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+ }
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+ }
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+
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+ /* Scale the images down if required */
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+ if (scale > 1) {
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+ /* Generate simple low-pass filter */
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+ low_pass.kernel = (float*)malloc(scale*scale*sizeof(float));
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+ if (!low_pass.kernel) {
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+ free(ref_f);
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+ free(cmp_f);
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+ return INFINITY;
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+ }
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+ low_pass.w = low_pass.h = scale;
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+ low_pass.normalized = 0;
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+ low_pass.bnd_opt = KBND_SYMMETRIC;
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+ for (offset=0; offset<scale*scale; ++offset)
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+ low_pass.kernel[offset] = 1.0f/(scale*scale);
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+
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+ /* Resample */
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+ if (_iqa_decimate(ref_f, w, h, scale, &low_pass, 0, 0, 0) ||
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+ _iqa_decimate(cmp_f, w, h, scale, &low_pass, 0, &w, &h)) { /* Update w/h */
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+ free(ref_f);
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+ free(cmp_f);
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+ free(low_pass.kernel);
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+ return INFINITY;
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+ }
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+ free(low_pass.kernel);
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+ }
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+
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+ result = _iqa_ssim(ref_f, cmp_f, w, h, &window, &mr, args);
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+
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+ free(ref_f);
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+ free(cmp_f);
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+
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+ return result;
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+}
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+
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+
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+/* _iqa_ssim */
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+float _iqa_ssim(float *ref, float *cmp, int w, int h, const struct _kernel *k, const struct _map_reduce *mr, const struct iqa_ssim_args *args)
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+{
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+ float alpha=1.0f, beta=1.0f, gamma=1.0f;
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+ int L=255;
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+ float K1=0.01f, K2=0.03f;
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+ float C1,C2,C3;
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+ int x,y,offset;
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+ float *ref_mu,*cmp_mu,*ref_sigma_sqd,*cmp_sigma_sqd,*sigma_both;
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+ double ssim_sum, numerator, denominator;
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+ double luminance_comp, contrast_comp, structure_comp, sigma_root;
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+ struct _ssim_int sint;
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+
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+ /* Initialize algorithm parameters */
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+ if (args) {
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+ if (!mr)
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+ return INFINITY;
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+ alpha = args->alpha;
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+ beta = args->beta;
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+ gamma = args->gamma;
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+ L = args->L;
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+ K1 = args->K1;
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+ K2 = args->K2;
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+ }
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+ C1 = (K1*L)*(K1*L);
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+ C2 = (K2*L)*(K2*L);
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+ C3 = C2 / 2.0f;
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+
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+ ref_mu = (float*)malloc(w*h*sizeof(float));
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+ cmp_mu = (float*)malloc(w*h*sizeof(float));
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+ ref_sigma_sqd = (float*)malloc(w*h*sizeof(float));
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+ cmp_sigma_sqd = (float*)malloc(w*h*sizeof(float));
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+ sigma_both = (float*)malloc(w*h*sizeof(float));
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+ if (!ref_mu || !cmp_mu || !ref_sigma_sqd || !cmp_sigma_sqd || !sigma_both) {
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+ if (ref_mu) free(ref_mu);
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+ if (cmp_mu) free(cmp_mu);
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+ if (ref_sigma_sqd) free(ref_sigma_sqd);
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+ if (cmp_sigma_sqd) free(cmp_sigma_sqd);
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+ if (sigma_both) free(sigma_both);
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+ return INFINITY;
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+ }
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+
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+ /* Calculate mean */
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+ _iqa_convolve(ref, w, h, k, ref_mu, 0, 0);
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+ _iqa_convolve(cmp, w, h, k, cmp_mu, 0, 0);
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+
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+ for (y=0; y<h; ++y) {
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+ offset = y*w;
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+ for (x=0; x<w; ++x, ++offset) {
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+ ref_sigma_sqd[offset] = ref[offset] * ref[offset];
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+ cmp_sigma_sqd[offset] = cmp[offset] * cmp[offset];
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+ sigma_both[offset] = ref[offset] * cmp[offset];
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+ }
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+ }
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+
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+ /* Calculate sigma */
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+ _iqa_convolve(ref_sigma_sqd, w, h, k, 0, 0, 0);
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+ _iqa_convolve(cmp_sigma_sqd, w, h, k, 0, 0, 0);
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+ _iqa_convolve(sigma_both, w, h, k, 0, &w, &h); /* Update the width and height */
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+
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+ /* The convolution results are smaller by the kernel width and height */
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+ for (y=0; y<h; ++y) {
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+ offset = y*w;
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+ for (x=0; x<w; ++x, ++offset) {
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+ ref_sigma_sqd[offset] -= ref_mu[offset] * ref_mu[offset];
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+ cmp_sigma_sqd[offset] -= cmp_mu[offset] * cmp_mu[offset];
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+ sigma_both[offset] -= ref_mu[offset] * cmp_mu[offset];
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+ }
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+ }
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+
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+ ssim_sum = 0.0;
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+ for (y=0; y<h; ++y) {
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+ offset = y*w;
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+ for (x=0; x<w; ++x, ++offset) {
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+
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+ if (!args) {
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+ /* The default case */
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+ numerator = (2.0 * ref_mu[offset] * cmp_mu[offset] + C1) * (2.0 * sigma_both[offset] + C2);
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+ denominator = (ref_mu[offset]*ref_mu[offset] + cmp_mu[offset]*cmp_mu[offset] + C1) *
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+ (ref_sigma_sqd[offset] + cmp_sigma_sqd[offset] + C2);
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+ ssim_sum += numerator / denominator;
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+ }
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+ else {
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+ /* User tweaked alpha, beta, or gamma */
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+
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+ /* passing a negative number to sqrt() cause a domain error */
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+ if (ref_sigma_sqd[offset] < 0.0f)
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+ ref_sigma_sqd[offset] = 0.0f;
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+ if (cmp_sigma_sqd[offset] < 0.0f)
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+ cmp_sigma_sqd[offset] = 0.0f;
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+ sigma_root = sqrt(ref_sigma_sqd[offset] * cmp_sigma_sqd[offset]);
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+
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+ luminance_comp = _calc_luminance(ref_mu[offset], cmp_mu[offset], C1, alpha);
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+ contrast_comp = _calc_contrast(sigma_root, ref_sigma_sqd[offset], cmp_sigma_sqd[offset], C2, beta);
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+ structure_comp = _calc_structure(sigma_both[offset], sigma_root, ref_sigma_sqd[offset], cmp_sigma_sqd[offset], C3, gamma);
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+
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+ sint.l = luminance_comp;
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+ sint.c = contrast_comp;
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+ sint.s = structure_comp;
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+
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+ if (mr->map(&sint, mr->context))
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+ return INFINITY;
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+ }
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+ }
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+ }
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+
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+ free(ref_mu);
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+ free(cmp_mu);
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+ free(ref_sigma_sqd);
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+ free(cmp_sigma_sqd);
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+ free(sigma_both);
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+
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+ if (!args)
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+ return (float)(ssim_sum / (double)(w*h));
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+ return mr->reduce(w, h, mr->context);
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+}
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+
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+
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+/* _ssim_map */
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+int _ssim_map(const struct _ssim_int *si, void *ctx)
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+{
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+ double *ssim_sum = (double*)ctx;
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+ *ssim_sum += si->l * si->c * si->s;
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+ return 0;
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+}
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+
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+/* _ssim_reduce */
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+float _ssim_reduce(int w, int h, void *ctx)
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+{
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+ double *ssim_sum = (double*)ctx;
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+ return (float)(*ssim_sum / (double)(w*h));
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+}
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+
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+
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+/* _calc_luminance */
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+IQA_INLINE static double _calc_luminance(float mu1, float mu2, float C1, float alpha)
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+{
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+ double result;
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+ float sign;
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+ /* For MS-SSIM* */
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+ if (C1 == 0 && mu1*mu1 == 0 && mu2*mu2 == 0)
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+ return 1.0;
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+ result = (2.0 * mu1 * mu2 + C1) / (mu1*mu1 + mu2*mu2 + C1);
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+ if (alpha == 1.0f)
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+ return result;
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+ sign = result < 0.0 ? -1.0f : 1.0f;
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+ return sign * pow(fabs(result),(double)alpha);
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+}
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+
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+/* _calc_contrast */
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+IQA_INLINE static double _calc_contrast(double sigma_comb_12, float sigma1_sqd, float sigma2_sqd, float C2, float beta)
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+{
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+ double result;
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+ float sign;
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+ /* For MS-SSIM* */
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+ if (C2 == 0 && sigma1_sqd + sigma2_sqd == 0)
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+ return 1.0;
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+ result = (2.0 * sigma_comb_12 + C2) / (sigma1_sqd + sigma2_sqd + C2);
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+ if (beta == 1.0f)
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+ return result;
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+ sign = result < 0.0 ? -1.0f : 1.0f;
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+ return sign * pow(fabs(result),(double)beta);
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+}
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+
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+/* _calc_structure */
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+IQA_INLINE static double _calc_structure(float sigma_12, double sigma_comb_12, float sigma1, float sigma2, float C3, float gamma)
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+{
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+ double result;
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+ float sign;
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+ /* For MS-SSIM* */
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+ if (C3 == 0 && sigma_comb_12 == 0) {
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+ if (sigma1 == 0 && sigma2 == 0)
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+ return 1.0;
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+ else if (sigma1 == 0 || sigma2 == 0)
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+ return 0.0;
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+ }
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+ result = (sigma_12 + C3) / (sigma_comb_12 + C3);
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+ if (gamma == 1.0f)
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+ return result;
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+ sign = result < 0.0 ? -1.0f : 1.0f;
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+ return sign * pow(fabs(result),(double)gamma);
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+}
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