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// 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