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enc_noise.cc (13342B)

---

// Copyright (c) the JPEG XL 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.

#include "lib/jxl/enc_noise.h"

#include <algorithm>
#include <cstdint>
#include <cstdlib>
#include <numeric>
#include <utility>

#include "lib/jxl/base/status.h"
#include "lib/jxl/enc_aux_out.h"
#include "lib/jxl/enc_optimize.h"

namespace jxl {
namespace {

using OptimizeArray = optimize::Array<double, NoiseParams::kNumNoisePoints>;

float GetScoreSumsOfAbsoluteDifferences(const Image3F& opsin, const int x,
                                       const int y, const int block_size) {
 const int small_bl_size_x = 3;
 const int small_bl_size_y = 4;
 const int kNumSAD =
     (block_size - small_bl_size_x) * (block_size - small_bl_size_y);
 // block_size x block_size reference pixels
 int counter = 0;
 const int offset = 2;

 std::vector<float> sad(kNumSAD, 0);
 for (int y_bl = 0; y_bl + small_bl_size_y < block_size; ++y_bl) {
   for (int x_bl = 0; x_bl + small_bl_size_x < block_size; ++x_bl) {
     float sad_sum = 0;
     // size of the center patch, we compare all the patches inside window with
     // the center one
     for (int cy = 0; cy < small_bl_size_y; ++cy) {
       for (int cx = 0; cx < small_bl_size_x; ++cx) {
         float wnd = 0.5f * (opsin.PlaneRow(1, y + y_bl + cy)[x + x_bl + cx] +
                             opsin.PlaneRow(0, y + y_bl + cy)[x + x_bl + cx]);
         float center =
             0.5f * (opsin.PlaneRow(1, y + offset + cy)[x + offset + cx] +
                     opsin.PlaneRow(0, y + offset + cy)[x + offset + cx]);
         sad_sum += std::abs(center - wnd);
       }
     }
     sad[counter++] = sad_sum;
   }
 }
 const int kSamples = (kNumSAD) / 2;
 // As with ROAD (rank order absolute distance), we keep the smallest half of
 // the values in SAD (we use here the more robust patch SAD instead of
 // absolute single-pixel differences).
 std::sort(sad.begin(), sad.end());
 const float total_sad_sum =
     std::accumulate(sad.begin(), sad.begin() + kSamples, 0.0f);
 return total_sad_sum / kSamples;
}

class NoiseHistogram {
public:
 static constexpr int kBins = 256;

 NoiseHistogram() { std::fill(bins, bins + kBins, 0); }

 void Increment(const float x) { bins[Index(x)] += 1; }
 int Get(const float x) const { return bins[Index(x)]; }
 int Bin(const size_t bin) const { return bins[bin]; }

 int Mode() const {
   size_t max_idx = 0;
   for (size_t i = 0; i < kBins; i++) {
     if (bins[i] > bins[max_idx]) max_idx = i;
   }
   return max_idx;
 }

 double Quantile(double q01) const {
   const int64_t total = std::accumulate(bins, bins + kBins, int64_t{1});
   const int64_t target = static_cast<int64_t>(q01 * total);
   // Until sum >= target:
   int64_t sum = 0;
   size_t i = 0;
   for (; i < kBins; ++i) {
     sum += bins[i];
     // Exact match: assume middle of bin i
     if (sum == target) {
       return i + 0.5;
     }
     if (sum > target) break;
   }

   // Next non-empty bin (in case histogram is sparsely filled)
   size_t next = i + 1;
   while (next < kBins && bins[next] == 0) {
     ++next;
   }

   // Linear interpolation according to how far into next we went
   const double excess = target - sum;
   const double weight_next = bins[Index(next)] / excess;
   return ClampX(next * weight_next + i * (1.0 - weight_next));
 }

 // Inter-quartile range
 double IQR() const { return Quantile(0.75) - Quantile(0.25); }

private:
 template <typename T>
 T ClampX(const T x) const {
   return std::min(std::max(static_cast<T>(0), x), static_cast<T>(kBins - 1));
 }
 size_t Index(const float x) const { return ClampX(static_cast<int>(x)); }

 uint32_t bins[kBins];
};

std::vector<float> GetSADScoresForPatches(const Image3F& opsin,
                                         const size_t block_s,
                                         const size_t num_bin,
                                         NoiseHistogram* sad_histogram) {
 std::vector<float> sad_scores(
     (opsin.ysize() / block_s) * (opsin.xsize() / block_s), 0.0f);

 int block_index = 0;

 for (size_t y = 0; y + block_s <= opsin.ysize(); y += block_s) {
   for (size_t x = 0; x + block_s <= opsin.xsize(); x += block_s) {
     float sad_sc = GetScoreSumsOfAbsoluteDifferences(opsin, x, y, block_s);
     sad_scores[block_index++] = sad_sc;
     sad_histogram->Increment(sad_sc * num_bin);
   }
 }
 return sad_scores;
}

float GetSADThreshold(const NoiseHistogram& histogram, const int num_bin) {
 // Here we assume that the most patches with similar SAD value is a "flat"
 // patches. However, some images might contain regular texture part and
 // generate second strong peak at the histogram
 // TODO(user) handle bimodal and heavy-tailed case
 const int mode = histogram.Mode();
 return static_cast<float>(mode) / NoiseHistogram::kBins;
}

// loss = sum asym * (F(x) - nl)^2 + kReg * num_points * sum (w[i] - w[i+1])^2
// where asym = 1 if F(x) < nl, kAsym if F(x) > nl.
struct LossFunction {
 explicit LossFunction(std::vector<NoiseLevel> nl0) : nl(std::move(nl0)) {}

 double Compute(const OptimizeArray& w, OptimizeArray* df,
                bool skip_regularization = false) const {
   constexpr double kReg = 0.005;
   constexpr double kAsym = 1.1;
   double loss_function = 0;
   for (size_t i = 0; i < w.size(); i++) {
     (*df)[i] = 0;
   }
   for (auto ind : nl) {
     std::pair<int, float> pos = IndexAndFrac(ind.intensity);
     JXL_DASSERT(pos.first >= 0 && static_cast<size_t>(pos.first) <
                                       NoiseParams::kNumNoisePoints - 1);
     double low = w[pos.first];
     double hi = w[pos.first + 1];
     double val = low * (1.0f - pos.second) + hi * pos.second;
     double dist = val - ind.noise_level;
     if (dist > 0) {
       loss_function += kAsym * dist * dist;
       (*df)[pos.first] -= kAsym * (1.0f - pos.second) * dist;
       (*df)[pos.first + 1] -= kAsym * pos.second * dist;
     } else {
       loss_function += dist * dist;
       (*df)[pos.first] -= (1.0f - pos.second) * dist;
       (*df)[pos.first + 1] -= pos.second * dist;
     }
   }
   if (skip_regularization) return loss_function;
   for (size_t i = 0; i + 1 < w.size(); i++) {
     double diff = w[i] - w[i + 1];
     loss_function += kReg * nl.size() * diff * diff;
     (*df)[i] -= kReg * diff * nl.size();
     (*df)[i + 1] += kReg * diff * nl.size();
   }
   return loss_function;
 }

 std::vector<NoiseLevel> nl;
};

void OptimizeNoiseParameters(const std::vector<NoiseLevel>& noise_level,
                            NoiseParams* noise_params) {
 constexpr double kMaxError = 1e-3;
 static const double kPrecision = 1e-8;
 static const int kMaxIter = 40;

 float avg = 0;
 for (const NoiseLevel& nl : noise_level) {
   avg += nl.noise_level;
 }
 avg /= noise_level.size();

 LossFunction loss_function(noise_level);
 OptimizeArray parameter_vector;
 for (size_t i = 0; i < parameter_vector.size(); i++) {
   parameter_vector[i] = avg;
 }

 parameter_vector = optimize::OptimizeWithScaledConjugateGradientMethod(
     loss_function, parameter_vector, kPrecision, kMaxIter);

 OptimizeArray df = parameter_vector;
 float loss = loss_function.Compute(parameter_vector, &df,
                                    /*skip_regularization=*/true) /
              noise_level.size();

 // Approximation went too badly: escape with no noise at all.
 if (loss > kMaxError) {
   noise_params->Clear();
   return;
 }

 for (size_t i = 0; i < parameter_vector.size(); i++) {
   noise_params->lut[i] = std::max(parameter_vector[i], 0.0);
 }
}

std::vector<NoiseLevel> GetNoiseLevel(
   const Image3F& opsin, const std::vector<float>& texture_strength,
   const float threshold, const size_t block_s) {
 std::vector<NoiseLevel> noise_level_per_intensity;

 const int filt_size = 1;
 static const float kLaplFilter[filt_size * 2 + 1][filt_size * 2 + 1] = {
     {-0.25f, -1.0f, -0.25f},
     {-1.0f, 5.0f, -1.0f},
     {-0.25f, -1.0f, -0.25f},
 };

 // The noise model is built based on channel 0.5 * (X+Y) as we notice that it
 // is similar to the model 0.5 * (Y-X)
 size_t patch_index = 0;

 for (size_t y = 0; y + block_s <= opsin.ysize(); y += block_s) {
   for (size_t x = 0; x + block_s <= opsin.xsize(); x += block_s) {
     if (texture_strength[patch_index] <= threshold) {
       // Calculate mean value
       float mean_int = 0;
       for (size_t y_bl = 0; y_bl < block_s; ++y_bl) {
         for (size_t x_bl = 0; x_bl < block_s; ++x_bl) {
           mean_int += 0.5f * (opsin.PlaneRow(1, y + y_bl)[x + x_bl] +
                               opsin.PlaneRow(0, y + y_bl)[x + x_bl]);
         }
       }
       mean_int /= block_s * block_s;

       // Calculate Noise level
       float noise_level = 0;
       size_t count = 0;
       for (size_t y_bl = 0; y_bl < block_s; ++y_bl) {
         for (size_t x_bl = 0; x_bl < block_s; ++x_bl) {
           float filtered_value = 0;
           for (int y_f = -1 * filt_size; y_f <= filt_size; ++y_f) {
             if ((static_cast<ssize_t>(y_bl) + y_f) >= 0 &&
                 (y_bl + y_f) < block_s) {
               for (int x_f = -1 * filt_size; x_f <= filt_size; ++x_f) {
                 if ((static_cast<ssize_t>(x_bl) + x_f) >= 0 &&
                     (x_bl + x_f) < block_s) {
                   filtered_value +=
                       0.5f *
                       (opsin.PlaneRow(1, y + y_bl + y_f)[x + x_bl + x_f] +
                        opsin.PlaneRow(0, y + y_bl + y_f)[x + x_bl + x_f]) *
                       kLaplFilter[y_f + filt_size][x_f + filt_size];
                 } else {
                   filtered_value +=
                       0.5f *
                       (opsin.PlaneRow(1, y + y_bl + y_f)[x + x_bl - x_f] +
                        opsin.PlaneRow(0, y + y_bl + y_f)[x + x_bl - x_f]) *
                       kLaplFilter[y_f + filt_size][x_f + filt_size];
                 }
               }
             } else {
               for (int x_f = -1 * filt_size; x_f <= filt_size; ++x_f) {
                 if ((static_cast<ssize_t>(x_bl) + x_f) >= 0 &&
                     (x_bl + x_f) < block_s) {
                   filtered_value +=
                       0.5f *
                       (opsin.PlaneRow(1, y + y_bl - y_f)[x + x_bl + x_f] +
                        opsin.PlaneRow(0, y + y_bl - y_f)[x + x_bl + x_f]) *
                       kLaplFilter[y_f + filt_size][x_f + filt_size];
                 } else {
                   filtered_value +=
                       0.5f *
                       (opsin.PlaneRow(1, y + y_bl - y_f)[x + x_bl - x_f] +
                        opsin.PlaneRow(0, y + y_bl - y_f)[x + x_bl - x_f]) *
                       kLaplFilter[y_f + filt_size][x_f + filt_size];
                 }
               }
             }
           }
           noise_level += std::abs(filtered_value);
           ++count;
         }
       }
       noise_level /= count;
       NoiseLevel nl;
       nl.intensity = mean_int;
       nl.noise_level = noise_level;
       noise_level_per_intensity.push_back(nl);
     }
     ++patch_index;
   }
 }
 return noise_level_per_intensity;
}

Status EncodeFloatParam(float val, float precision, BitWriter* writer) {
 JXL_ENSURE(val >= 0);
 const int absval_quant = static_cast<int>(std::lround(val * precision));
 JXL_ENSURE(absval_quant < (1 << 10));
 writer->Write(10, absval_quant);
 return true;
}

}  // namespace

Status GetNoiseParameter(const Image3F& opsin, NoiseParams* noise_params,
                        float quality_coef) {
 // The size of a patch in decoder might be different from encoder's patch
 // size.
 // For encoder: the patch size should be big enough to estimate
 //              noise level, but, at the same time, it should be not too big
 //              to be able to estimate intensity value of the patch
 const size_t block_s = 8;
 const size_t kNumBin = 256;
 NoiseHistogram sad_histogram;
 std::vector<float> sad_scores =
     GetSADScoresForPatches(opsin, block_s, kNumBin, &sad_histogram);
 float sad_threshold = GetSADThreshold(sad_histogram, kNumBin);
 // If threshold is too large, the image has a strong pattern. This pattern
 // fools our model and it will add too much noise. Therefore, we do not add
 // noise for such images
 if (sad_threshold > 0.15f || sad_threshold <= 0.0f) {
   noise_params->Clear();
   return false;
 }
 std::vector<NoiseLevel> nl =
     GetNoiseLevel(opsin, sad_scores, sad_threshold, block_s);

 OptimizeNoiseParameters(nl, noise_params);
 for (float& i : noise_params->lut) {
   i *= quality_coef * 1.4;
 }
 return noise_params->HasAny();
}

Status EncodeNoise(const NoiseParams& noise_params, BitWriter* writer,
                  LayerType layer, AuxOut* aux_out) {
 JXL_ENSURE(noise_params.HasAny());

 return writer->WithMaxBits(
     NoiseParams::kNumNoisePoints * 16, layer, aux_out, [&]() -> Status {
       for (float i : noise_params.lut) {
         JXL_RETURN_IF_ERROR(EncodeFloatParam(i, kNoisePrecision, writer));
       }
       return true;
     });
}

}  // namespace jxl