Implemented NSIM similarity measurement.

- Implemented NSIM (DOI:10.1016/j.specom.2011.09.004).
- Replaced the geometric norm calculation across time and frequency axes
  with '1 - NSIM' when computing Zimtohrli distance.
- Removed the redundant cpp/zimt/README.md.
- Refactored the dataset management tools to enable optimization without
  saving the intermediary results.
- Implemented simple simulated annealing optimization for some relevant
  Zimtohrli parameters.
- Redid the MOS mapping so that Zimtohrli MOS scores are still on the
  same scale as before the NSIM change.

Before:

|Score type |MSE  |Min score |Max score |Mean score |
|-----------|-----|----------|----------|-----------|
|ViSQOL     |0.09 |0.52      |0.80      |0.62       |
|PESQ       |0.10 |0.48      |0.84      |0.61       |
|Zimtohrli  |0.10 |0.56      |0.74      |0.59       |
|CDPAM      |0.12 |0.44      |0.73      |0.57       |
|PARLAQ     |0.15 |0.47      |0.78      |0.54       |
|PEAQB      |0.18 |0.28      |0.85      |0.51       |
|DPAM       |0.28 |0.19      |0.69      |0.42       |
|WARP-Q     |0.28 |0.07      |0.78      |0.45       |
|GVPMOS     |0.32 |0.01      |0.78      |0.40       |

After:

|Score type |MSE  |Min score |Max score |Mean score |
|-----------|-----|----------|----------|-----------|
|ViSQOL     |0.09 |0.52      |0.80      |0.62       |
|Zimtohrli  |0.09 |0.59      |0.72      |0.60       |
|PESQ       |0.10 |0.48      |0.84      |0.61       |
|CDPAM      |0.12 |0.44      |0.73      |0.57       |
|PARLAQ     |0.15 |0.47      |0.78      |0.54       |
|PEAQB      |0.18 |0.28      |0.85      |0.51       |
|DPAM       |0.28 |0.19      |0.69      |0.42       |
|WARP-Q     |0.28 |0.07      |0.78      |0.45       |
|GVPMOS     |0.32 |0.01      |0.78      |0.40       |

CMakeLists.txt

@@ -26,6 +26,8 @@ add_library(zimtohrli_base STATIC
     cpp/zimt/masking.h
     cpp/zimt/mos.cc
     cpp/zimt/mos.h
+    cpp/zimt/nsim.cc
+    cpp/zimt/nsim.h
     cpp/zimt/zimtohrli.cc
     cpp/zimt/zimtohrli.h
 )

cmake/tests.cmake

@@ -7,6 +7,7 @@ add_executable(zimtohrli_test
     cpp/zimt/loudness_test.cc
     cpp/zimt/masking_test.cc
     cpp/zimt/mos_test.cc
+    cpp/zimt/nsim_test.cc
     cpp/zimt/zimtohrli_test.cc
     cpp/zimt/test_file_paths.cc
 )
@@ -54,6 +55,7 @@ add_executable(zimtohrli_benchmark
     cpp/zimt/filterbank_test.cc
     cpp/zimt/loudness_test.cc
     cpp/zimt/masking_test.cc
+    cpp/zimt/nsim_test.cc
     cpp/zimt/zimtohrli_test.cc
 )
 target_link_libraries(zimtohrli_benchmark zimtohrli_base gtest gmock benchmark_main)

configure.sh

@@ -5,7 +5,7 @@ if [ "${1}" == "debug" ]; then
     (cd debug_build && cmake -G Ninja -DCMAKE_C_FLAGS='-fPIC' -DCMAKE_CXX_FLAGS='-fPIC' -DCMAKE_BUILD_TYPE=RelWithDebInfo ..)
 elif [ "${1}" == "asan" ]; then
     mkdir -p asan_build
-    (cd asan_build && cmake -G Ninja -DCMAKE_C_FLAGS='-fPIC' -DZIMTOHRLI_ASAN=1 -DCMAKE_CXX_FLAGS='-fPIC' -DCMAKE_BUILD_TYPE=RelWithDebInfo ..)
+    (cd asan_build && cmake -G Ninja -DCMAKE_C_FLAGS='-fsanitize=address -fPIC' -DCMAKE_CXX_FLAGS='-fsanitize=address -fPIC' -DCMAKE_LINKER_FLAGS_DEBUG='-fsanitize=address' -DCMAKE_BUILD_TYPE=RelWithDebInfo ..)
 else
     mkdir -p build
     (cd build && cmake -G Ninja -DCMAKE_C_FLAGS='-fPIC' -DCMAKE_CXX_FLAGS='-fPIC' -DCMAKE_BUILD_TYPE=Release ..)

cpp/zimt/compare.cc

@@ -75,10 +75,6 @@ ABSL_FLAG(bool, truncate, false,
 ABSL_FLAG(float, unwarp_window, 2.0f,
           "unwarp window length in seconds, must be greater than 0 if truncate "
           "is false and the files are of different lengths");
-ABSL_FLAG(float, freq_norm_order, zimtohrli::Zimtohrli{}.freq_norm_order,
-          "order of the per-step-norm across frequencies");
-ABSL_FLAG(float, time_norm_order, zimtohrli::Zimtohrli{}.time_norm_order,
-          "order of the norm across all time steps");
 ABSL_FLAG(bool, normalize_amplitude, true,
           "whether to normalize the amplitude of all B sounds to the same max "
           "amplitude as the A sound");
@@ -278,8 +274,6 @@ int Main(int argc, char* argv[]) {
       .perceptual_sample_rate = absl::GetFlag(FLAGS_perceptual_sample_rate),
       .cam_filterbank =
           cam.CreateFilterbank(static_cast<float>(file_a->Info().samplerate)),
-      .time_norm_order = absl::GetFlag(FLAGS_time_norm_order),
-      .freq_norm_order = absl::GetFlag(FLAGS_freq_norm_order),
       .full_scale_sine_db = absl::GetFlag(FLAGS_full_scale_sine_db),
   };
 

cpp/zimt/goohrli.cc

@@ -35,6 +35,12 @@ float DefaultPerceptualSampleRate() {
   return zimtohrli::Zimtohrli{}.perceptual_sample_rate;
 }
 
+int DefaultNSIMStepWindow() { return zimtohrli::Zimtohrli{}.nsim_step_window; }
+
+int DefaultNSIMChannelWindow() {
+  return zimtohrli::Zimtohrli{}.nsim_channel_window;
+}
+
 EnergyAndMaxAbsAmplitude Measure(const float* signal, int size) {
   hwy::AlignedNDArray<float, 1> signal_array({static_cast<size_t>(size)});
   hwy::CopyBytes(signal, signal_array.data(), size * sizeof(float));
@@ -99,20 +105,24 @@ float AnalysisDistance(Zimtohrli zimtohrli, Analysis a, Analysis b,
       .value;
 }
 
-float GetTimeNormOrder(Zimtohrli zimtohrli) {
-  return static_cast<zimtohrli::Zimtohrli*>(zimtohrli)->time_norm_order;
+int GetNSIMStepWindow(Zimtohrli zimtohrli) {
+  return static_cast<int>(
+      static_cast<zimtohrli::Zimtohrli*>(zimtohrli)->nsim_step_window);
 }
 
-void SetTimeNormOrder(Zimtohrli zimtohrli, float f) {
-  static_cast<zimtohrli::Zimtohrli*>(zimtohrli)->time_norm_order = f;
+void SetNSIMStepWindow(Zimtohrli zimtohrli, int s) {
+  static_cast<zimtohrli::Zimtohrli*>(zimtohrli)->nsim_step_window =
+      static_cast<size_t>(s);
 }
 
-float GetFreqNormOrder(Zimtohrli zimtohrli) {
-  return static_cast<zimtohrli::Zimtohrli*>(zimtohrli)->freq_norm_order;
+int GetNSIMChannelWindow(Zimtohrli zimtohrli) {
+  return static_cast<int>(
+      static_cast<zimtohrli::Zimtohrli*>(zimtohrli)->nsim_channel_window);
 }
 
-void SetFreqNormOrder(Zimtohrli zimtohrli, float f) {
-  static_cast<zimtohrli::Zimtohrli*>(zimtohrli)->freq_norm_order = f;
+void SetNSIMChannelWindow(Zimtohrli zimtohrli, int s) {
+  static_cast<zimtohrli::Zimtohrli*>(zimtohrli)->nsim_channel_window =
+      static_cast<size_t>(s);
 }
 
 float GetPerceptualSampleRate(Zimtohrli zimtohrli) {

cpp/zimt/mos.cc

@@ -19,19 +19,21 @@
 
 namespace zimtohrli {
 
-const std::array<float, 4> params = {3.439e+00, -4.138e-02, 3.008e+00,
-                                     -1.354e-01};
-
 namespace {
 
-float sigmoid(float x) { return 1 / (1 + std::exp(-x)); }
+const std::array<float, 3> params = {1.000e+00, 7.451e-09, 2.943e+00};
+
+float sigmoid(float x) {
+  return params[0] / (params[1] + std::exp(params[2] * x));
+}
+
+const float zero_crossing_reciprocal = 1.0 / sigmoid(0);
 
 }  // namespace
 
 // Optimized using `mos_mapping.ipynb`.
 float MOSFromZimtohrli(float zimtohrli_distance) {
-  return 1 + 2 * (sigmoid(params[0] + params[1] * zimtohrli_distance) +
-                  sigmoid(params[2] + params[3] * zimtohrli_distance));
+  return 1.0 + 4.0 * sigmoid(zimtohrli_distance) * zero_crossing_reciprocal;
 }
 
 }  // namespace zimtohrli

cpp/zimt/mos_test.cc

@@ -24,9 +24,9 @@ namespace zimtohrli {
 namespace {
 
 TEST(MOS, MOSFromZimtohrli) {
-  const std::vector<float> zimt_scores = {5, 20, 40, 80};
-  const std::vector<float> mos = {4.746790024702545, 4.01181593706087,
-                                  2.8773086764995064, 2.0648331964917945};
+  const std::vector<float> zimt_scores = {0, 0.1, 0.5, 0.7, 1.0};
+  const std::vector<float> mos = {5.0, 3.9802114963531494, 1.9183233976364136,
+                                  1.5097649097442627, 1.210829496383667};
   for (size_t index = 0; index < zimt_scores.size(); ++index) {
     ASSERT_NEAR(MOSFromZimtohrli(zimt_scores[index]), mos[index], 1e-2);
   }