Merge pull request #9249 from hrnr:akaze_part3

[GSOC] Speeding-up AKAZE, part #3 (#9249)

* use finding of scale extremas from fast_akaze

* incorporade finding of extremas and subpixel refinement from Hideaki Suzuki's fast_akaze (https://github.com/h2suzuki/fast_akaze)
* use opencv parallel framework
* do not search for keypoints near the border, where we can't compute sensible descriptors (bugs fixed in ffd9ad99f4946e31508677dab09bddbecb82ae9f, 2c5389594bb560b62097de3602755ef97e60135f), but the descriptors were not 100% correct. this is a better solution

this version produces less keypoints with the same treshold. It is more effective in pruning similar keypoints (which do not bring any new information), so we have less keypoints, but with high quality. Accuracy is about the same.

* incorporate bugfix from upstream

* fix bug in subpixel refinement
* see commit db3dc22981e856ca8111f2f7fe57d9c2e0286efc in Pablo's repo

* rework finding of scale space extremas

* store just keypoints positions
* store positions in uchar mask for effective spatial search for neighbours
* construct keypoints structs at the very end

* lower inlier threshold in test

* win32 has lower accuracy

modules/features2d/src/kaze/AKAZEFeatures.cpp

@@ -49,6 +49,15 @@ void AKAZEFeatures::Allocate_Memory_Evolution(void) {
   float rfactor = 0.0f;
   int level_height = 0, level_width = 0;
 
+  // maximum size of the area for the descriptor computation
+  float smax = 0.0;
+  if (options_.descriptor == AKAZE::DESCRIPTOR_MLDB_UPRIGHT || options_.descriptor == AKAZE::DESCRIPTOR_MLDB) {
+    smax = 10.0f*sqrtf(2.0f);
+  }
+  else if (options_.descriptor == AKAZE::DESCRIPTOR_KAZE_UPRIGHT || options_.descriptor == AKAZE::DESCRIPTOR_KAZE) {
+    smax = 12.0f*sqrtf(2.0f);
+  }
+
   // Allocate the dimension of the matrices for the evolution
   for (int i = 0, power = 1; i <= options_.omax - 1; i++, power *= 2) {
     rfactor = 1.0f / power;
@@ -70,6 +79,8 @@ void AKAZEFeatures::Allocate_Memory_Evolution(void) {
       step.octave = i;
       step.sublevel = j;
       step.octave_ratio = (float)power;
+      step.border = fRound(smax * step.sigma_size) + 1;
+
       evolution_.push_back(step);
     }
   }
@@ -477,20 +488,6 @@ void AKAZEFeatures::Create_Nonlinear_Scale_Space(InputArray img)
   return;
 }
 
-/* ************************************************************************* */
-/**
- * @brief This method selects interesting keypoints through the nonlinear scale space
- * @param kpts Vector of detected keypoints
- */
-void AKAZEFeatures::Feature_Detection(std::vector<KeyPoint>& kpts)
-{
-  CV_INSTRUMENT_REGION()
-
-  kpts.clear();
-  Find_Scale_Space_Extrema(kpts);
-  Do_Subpixel_Refinement(kpts);
-}
-
 /* ************************************************************************* */
 
 #ifdef HAVE_OPENCL
@@ -608,212 +605,271 @@ void AKAZEFeatures::Compute_Determinant_Hessian_Response(void) {
 }
 
 /* ************************************************************************* */
+
 /**
- * @brief This method finds extrema in the nonlinear scale space
+ * @brief This method selects interesting keypoints through the nonlinear scale space
  * @param kpts Vector of detected keypoints
  */
-void AKAZEFeatures::Find_Scale_Space_Extrema(std::vector<KeyPoint>& kpts)
+void AKAZEFeatures::Feature_Detection(std::vector<KeyPoint>& kpts)
 {
   CV_INSTRUMENT_REGION()
 
-  float value = 0.0;
-  float dist = 0.0, ratio = 0.0, smax = 0.0;
-  int npoints = 0, id_repeated = 0;
-  int sigma_size_ = 0, left_x = 0, right_x = 0, up_y = 0, down_y = 0;
-  bool is_extremum = false, is_repeated = false, is_out = false;
-  KeyPoint point;
-  vector<KeyPoint> kpts_aux;
+  kpts.clear();
+  std::vector<Mat> keypoints_by_layers;
+  Find_Scale_Space_Extrema(keypoints_by_layers);
+  Do_Subpixel_Refinement(keypoints_by_layers, kpts);
+}
 
-  // Set maximum size
-  if (options_.descriptor == AKAZE::DESCRIPTOR_MLDB_UPRIGHT || options_.descriptor == AKAZE::DESCRIPTOR_MLDB) {
-    smax = 10.0f*sqrtf(2.0f);
-  }
-  else if (options_.descriptor == AKAZE::DESCRIPTOR_KAZE_UPRIGHT || options_.descriptor == AKAZE::DESCRIPTOR_KAZE) {
-    smax = 12.0f*sqrtf(2.0f);
+/**
+ * @brief This method searches v for a neighbor point of the point candidate p
+ * @param x Coordinates of the keypoint candidate to search a neighbor
+ * @param y Coordinates of the keypoint candidate to search a neighbor
+ * @param mask Matrix holding keypoints positions
+ * @param search_radius neighbour radius for searching keypoints
+ * @param idx The index to mask, pointing to keypoint found.
+ * @return true if a neighbor point is found; false otherwise
+ */
+static inline bool
+find_neighbor_point(const int x, const int y, const Mat &mask, const int search_radius, int &idx)
+{
+  // search neighborhood for keypoints
+  for (int i = y - search_radius; i < y + search_radius; ++i) {
+    const uchar *curr = mask.ptr<uchar>(i);
+    for (int j = x - search_radius; j < x + search_radius; ++j) {
+      if (curr[j] == 0) {
+        continue; // skip non-keypoint
+      }
+      // fine-compare with L2 metric (L2 is smaller than our search window)
+      int dx = j - x;
+      int dy = i - y;
+      if (dx * dx + dy * dy <= search_radius * search_radius) {
+        idx = i * mask.cols + j;
+        return true;
+      }
+    }
   }
 
-  for (size_t i = 0; i < evolution_.size(); i++) {
-    Mat Ldet = evolution_[i].Mdet;
-    const float* prev = Ldet.ptr<float>(0);
-    const float* curr = Ldet.ptr<float>(1);
-    for (int ix = 1; ix < Ldet.rows - 1; ix++) {
-      const float* next = Ldet.ptr<float>(ix + 1);
-
-      for (int jx = 1; jx < Ldet.cols - 1; jx++) {
-        is_extremum = false;
-        is_repeated = false;
-        is_out = false;
-        value = *(Ldet.ptr<float>(ix)+jx);
-
-        // Filter the points with the detector threshold
-        if (value > options_.dthreshold && value >= options_.min_dthreshold &&
-            value > curr[jx-1] &&
-            value > curr[jx+1] &&
-            value > prev[jx-1] &&
-            value > prev[jx] &&
-            value > prev[jx+1] &&
-            value > next[jx-1] &&
-            value > next[jx] &&
-            value > next[jx+1]) {
-
-          is_extremum = true;
-          point.response = fabs(value);
-          point.size = evolution_[i].esigma*options_.derivative_factor;
-          point.octave = (int)evolution_[i].octave;
-          point.class_id = (int)i;
-          ratio = (float)fastpow(2, point.octave);
-          sigma_size_ = fRound(point.size / ratio);
-          point.pt.x = static_cast<float>(jx);
-          point.pt.y = static_cast<float>(ix);
-
-          // Compare response with the same and lower scale
-          for (size_t ik = 0; ik < kpts_aux.size(); ik++) {
-
-            if ((point.class_id - 1) == kpts_aux[ik].class_id ||
-                point.class_id == kpts_aux[ik].class_id) {
-              float distx = point.pt.x*ratio - kpts_aux[ik].pt.x;
-              float disty = point.pt.y*ratio - kpts_aux[ik].pt.y;
-              dist = distx * distx + disty * disty;
-              if (dist <= point.size * point.size) {
-                if (point.response > kpts_aux[ik].response) {
-                  id_repeated = (int)ik;
-                  is_repeated = true;
-                }
-                else {
-                  is_extremum = false;
-                }
-                break;
-              }
+  return false;
+}
+
+/**
+ * @brief Find keypoints in parallel for each pyramid layer
+ */
+class FindKeypointsSameScale : public ParallelLoopBody
+{
+public:
+    explicit FindKeypointsSameScale(const std::vector<Evolution>& ev,
+      std::vector<Mat>& kpts, float dthreshold)
+    : evolution_(&ev), keypoints_by_layers_(&kpts), dthreshold_(dthreshold)
+  {}
+
+  void operator()(const Range& range) const
+  {
+    for (int i = range.start; i < range.end; i++)
+    {
+      const Evolution &e = (*evolution_)[i];
+      Mat &kpts = (*keypoints_by_layers_)[i];
+      // this mask will hold positions of keypoints in this level
+      kpts = Mat::zeros(e.Mdet.size(), CV_8UC1);
+
+      // if border is too big we shouldn't search any keypoints
+      if (e.border + 1 >= e.Ldet.rows)
+        continue;
+
+      const float * prev = e.Mdet.ptr<float>(e.border - 1);
+      const float * curr = e.Mdet.ptr<float>(e.border    );
+      const float * next = e.Mdet.ptr<float>(e.border + 1);
+      const float * ldet = e.Mdet.ptr<float>();
+      uchar *mask = kpts.ptr<uchar>();
+      const int search_radius = e.sigma_size; // size of keypoint in this level
+
+      for (int y = e.border; y < e.Ldet.rows - e.border; y++) {
+        for (int x = e.border; x < e.Ldet.cols - e.border; x++) {
+          const float value = curr[x];
+
+          // Filter the points with the detector threshold
+          if (value <= dthreshold_)
+            continue;
+          if (value <= curr[x-1] || value <= curr[x+1])
+            continue;
+          if (value <= prev[x-1] || value <= prev[x  ] || value <= prev[x+1])
+            continue;
+          if (value <= next[x-1] || value <= next[x  ] || value <= next[x+1])
+            continue;
+
+          int idx = 0;
+          // Compare response with the same scale
+          if (find_neighbor_point(x, y, kpts, search_radius, idx)) {
+            if (value > ldet[idx]) {
+              mask[idx] = 0;  // clear old point - we have better candidate now
+            } else {
+              continue; // there already is a better keypoint
             }
           }
 
-          // Check out of bounds
-          if (is_extremum == true) {
+          kpts.at<uchar>(y, x) = 1; // we have a new keypoint
+        }
 
-            // Check that the point is under the image limits for the descriptor computation
-            left_x = fRound(point.pt.x - smax*sigma_size_) - 1;
-            right_x = fRound(point.pt.x + smax*sigma_size_) + 1;
-            up_y = fRound(point.pt.y - smax*sigma_size_) - 1;
-            down_y = fRound(point.pt.y + smax*sigma_size_) + 1;
+        prev = curr;
+        curr = next;
+        next += e.Ldet.cols;
+      }
+    }
+  }
 
-            if (left_x < 0 || right_x >= Ldet.cols ||
-                up_y < 0 || down_y >= Ldet.rows) {
-              is_out = true;
-            }
+private:
+  const std::vector<Evolution>*  evolution_;
+  std::vector<Mat>* keypoints_by_layers_;
+  float dthreshold_; ///< Detector response threshold to accept point
+};
 
-            if (is_out == false) {
-              if (is_repeated == false) {
-                point.pt.x = (float)(point.pt.x*ratio + .5*(ratio-1.0));
-                point.pt.y = (float)(point.pt.y*ratio + .5*(ratio-1.0));
-                kpts_aux.push_back(point);
-                npoints++;
-              }
-              else {
-                point.pt.x = (float)(point.pt.x*ratio + .5*(ratio-1.0));
-                point.pt.y = (float)(point.pt.y*ratio + .5*(ratio-1.0));
-                kpts_aux[id_repeated] = point;
-              }
-            } // if is_out
-          } //if is_extremum
+/**
+ * @brief This method finds extrema in the nonlinear scale space
+ * @param keypoints_by_layers Output vectors of detected keypoints; one vector for each evolution level
+ */
+void AKAZEFeatures::Find_Scale_Space_Extrema(std::vector<Mat>& keypoints_by_layers)
+{
+  CV_INSTRUMENT_REGION()
+
+  keypoints_by_layers.resize(evolution_.size());
+
+  // find points in the same level
+  parallel_for_(Range(0, (int)evolution_.size()),
+    FindKeypointsSameScale(evolution_, keypoints_by_layers, options_.dthreshold));
+
+  // Filter points with the lower scale level
+  for (size_t i = 1; i < keypoints_by_layers.size(); i++) {
+    // constants for this level
+    const Mat &keypoints = keypoints_by_layers[i];
+    const uchar *const kpts = keypoints_by_layers[i].ptr<uchar>();
+    uchar *const kpts_prev = keypoints_by_layers[i-1].ptr<uchar>();
+    const float *const ldet = evolution_[i].Mdet.ptr<float>();
+    const float *const ldet_prev = evolution_[i-1].Mdet.ptr<float>();
+    // ratios are just powers of 2
+    const int diff_ratio = (int)evolution_[i].octave_ratio / (int)evolution_[i-1].octave_ratio;
+    const int search_radius = evolution_[i].sigma_size * diff_ratio; // size of keypoint in this level
+
+    size_t j = 0;
+    for (int y = 0; y < keypoints.rows; y++) {
+      for (int x = 0; x < keypoints.cols; x++, j++) {
+        if (kpts[j] == 0) {
+          continue; // skip non-keypoints
         }
-      } // for jx
-      prev = curr;
-      curr = next;
-    } // for ix
-  } // for i
-
-  // Now filter points with the upper scale level
-  for (size_t i = 0; i < kpts_aux.size(); i++) {
-
-    is_repeated = false;
-    const KeyPoint& pt = kpts_aux[i];
-    for (size_t j = i + 1; j < kpts_aux.size(); j++) {
-
-      // Compare response with the upper scale
-      if ((pt.class_id + 1) == kpts_aux[j].class_id) {
-        float distx = pt.pt.x - kpts_aux[j].pt.x;
-        float disty = pt.pt.y - kpts_aux[j].pt.y;
-        dist = distx * distx + disty * disty;
-        if (dist <= pt.size * pt.size) {
-          if (pt.response < kpts_aux[j].response) {
-            is_repeated = true;
-            break;
+        int idx = 0;
+        // project point to lower scale layer
+        const int p_x = x * diff_ratio;
+        const int p_y = y * diff_ratio;
+        if (find_neighbor_point(p_x, p_y, keypoints_by_layers[i-1], search_radius, idx)) {
+          if (ldet[j] > ldet_prev[idx]) {
+            kpts_prev[idx] = 0;  // clear keypoint in lower layer
           }
+          // else this pt may be pruned by the upper scale
         }
       }
     }
+  }
 
-    if (is_repeated == false)
-      kpts.push_back(pt);
+  // Now filter points with the upper scale level (the other direction)
+  for (int i = (int)keypoints_by_layers.size() - 2; i >= 0; i--) {
+    // constants for this level
+    const Mat &keypoints = keypoints_by_layers[i];
+    const uchar *const kpts = keypoints_by_layers[i].ptr<uchar>();
+    uchar *const kpts_next = keypoints_by_layers[i+1].ptr<uchar>();
+    const float *const ldet = evolution_[i].Mdet.ptr<float>();
+    const float *const ldet_next = evolution_[i+1].Mdet.ptr<float>();
+    // ratios are just powers of 2, i+1 ratio is always greater or equal to i
+    const int diff_ratio = (int)evolution_[i+1].octave_ratio / (int)evolution_[i].octave_ratio;
+    const int search_radius = evolution_[i+1].sigma_size; // size of keypoints in upper level
+
+    size_t j = 0;
+    for (int y = 0; y < keypoints.rows; y++) {
+      for (int x = 0; x < keypoints.cols; x++, j++) {
+        if (kpts[j] == 0) {
+          continue; // skip non-keypoints
+        }
+        int idx = 0;
+        // project point to upper scale layer
+        const int p_x = x / diff_ratio;
+        const int p_y = y / diff_ratio;
+        if (find_neighbor_point(p_x, p_y, keypoints_by_layers[i+1], search_radius, idx)) {
+          if (ldet[j] > ldet_next[idx]) {
+            kpts_next[idx] = 0;  // clear keypoint in upper layer
+          }
+        }
+      }
+    }
   }
 }
 
 /* ************************************************************************* */
 /**
  * @brief This method performs subpixel refinement of the detected keypoints
- * @param kpts Vector of detected keypoints
+ * @param keypoints_by_layers Input vectors of detected keypoints, sorted by evolution levels
+ * @param kpts Output vector of the final refined keypoints
  */
-void AKAZEFeatures::Do_Subpixel_Refinement(std::vector<KeyPoint>& kpts)
+void AKAZEFeatures::Do_Subpixel_Refinement(
+  std::vector<Mat>& keypoints_by_layers, std::vector<KeyPoint>& output_keypoints)
 {
   CV_INSTRUMENT_REGION()
 
-  float Dx = 0.0, Dy = 0.0, ratio = 0.0;
-  float Dxx = 0.0, Dyy = 0.0, Dxy = 0.0;
-  int x = 0, y = 0;
-  Matx22f A(0, 0, 0, 0);
-  Vec2f b(0, 0);
-  Vec2f dst(0, 0);
-
-  for (size_t i = 0; i < kpts.size(); i++) {
-    ratio = (float)fastpow(2, kpts[i].octave);
-    x = fRound(kpts[i].pt.x / ratio);
-    y = fRound(kpts[i].pt.y / ratio);
-    Mat Ldet = evolution_[kpts[i].class_id].Mdet;
-
-    // Compute the gradient
-    Dx = (0.5f)*(*(Ldet.ptr<float>(y)+x + 1)
-        - *(Ldet.ptr<float>(y)+x - 1));
-    Dy = (0.5f)*(*(Ldet.ptr<float>(y + 1) + x)
-        - *(Ldet.ptr<float>(y - 1) + x));
-
-    // Compute the Hessian
-    Dxx = (*(Ldet.ptr<float>(y)+x + 1)
-        + *(Ldet.ptr<float>(y)+x - 1)
-        - 2.0f*(*(Ldet.ptr<float>(y)+x)));
-
-    Dyy = (*(Ldet.ptr<float>(y + 1) + x)
-        + *(Ldet.ptr<float>(y - 1) + x)
-        - 2.0f*(*(Ldet.ptr<float>(y)+x)));
-
-    Dxy = (0.25f)*(*(Ldet.ptr<float>(y + 1) + x + 1)
-        + (*(Ldet.ptr<float>(y - 1) + x - 1)))
-        - (0.25f)*(*(Ldet.ptr<float>(y - 1) + x + 1)
-        + (*(Ldet.ptr<float>(y + 1) + x - 1)));
-
-    // Solve the linear system
-    A(0, 0) = Dxx;
-    A(1, 1) = Dyy;
-    A(0, 1) = A(1, 0) = Dxy;
-    b(0) = -Dx;
-    b(1) = -Dy;
-
-    solve(A, b, dst, DECOMP_LU);
-
-    if (fabs(dst(0)) <= 1.0f && fabs(dst(1)) <= 1.0f) {
-        kpts[i].pt.x = x + dst(0);
-      kpts[i].pt.y = y + dst(1);
-      int power = fastpow(2, evolution_[kpts[i].class_id].octave);
-      kpts[i].pt.x = (float)(kpts[i].pt.x*power + .5*(power-1));
-      kpts[i].pt.y = (float)(kpts[i].pt.y*power + .5*(power-1));
-      kpts[i].angle = 0.0;
-
-      // In OpenCV the size of a keypoint its the diameter
-      kpts[i].size *= 2.0f;
-    }
-    // Delete the point since its not stable
-    else {
-      kpts.erase(kpts.begin() + i);
-      i--;
+  for (size_t i = 0; i < keypoints_by_layers.size(); i++) {
+    const Evolution &e = evolution_[i];
+    const float * const ldet = e.Mdet.ptr<float>();
+    const float ratio = e.octave_ratio;
+    const int cols = e.Ldet.cols;
+    const Mat& keypoints = keypoints_by_layers[i];
+    const uchar *const kpts = keypoints.ptr<uchar>();
+
+    size_t j = 0;
+    for (int y = 0; y < keypoints.rows; y++) {
+      for (int x = 0; x < keypoints.cols; x++, j++) {
+        if (kpts[j] == 0) {
+          continue; // skip non-keypoints
+        }
+
+        // create a new keypoint
+        KeyPoint kp;
+        kp.pt.x = x * e.octave_ratio;
+        kp.pt.y = y * e.octave_ratio;
+        kp.size = e.esigma * options_.derivative_factor;
+        kp.angle = -1;
+        kp.response = ldet[j];
+        kp.octave = e.octave;
+        kp.class_id = static_cast<int>(i);
+
+        // Compute the gradient
+        float Dx = 0.5f * (ldet[ y     *cols + x + 1] - ldet[ y     *cols + x - 1]);
+        float Dy = 0.5f * (ldet[(y + 1)*cols + x    ] - ldet[(y - 1)*cols + x    ]);
+
+        // Compute the Hessian
+        float Dxx = ldet[ y     *cols + x + 1] + ldet[ y     *cols + x - 1] - 2.0f * ldet[y*cols + x];
+        float Dyy = ldet[(y + 1)*cols + x    ] + ldet[(y - 1)*cols + x    ] - 2.0f * ldet[y*cols + x];
+        float Dxy = 0.25f * (ldet[(y + 1)*cols + x + 1] + ldet[(y - 1)*cols + x - 1] -
+                            ldet[(y - 1)*cols + x + 1] - ldet[(y + 1)*cols + x - 1]);
+
+        // Solve the linear system
+        Matx22f A( Dxx, Dxy,
+                   Dxy, Dyy );
+        Vec2f   b( -Dx, -Dy );
+        Vec2f   dst( 0.0f, 0.0f );
+        solve(A, b, dst, DECOMP_LU);
+
+        float dx = dst(0);
+        float dy = dst(1);
+
+        if (fabs(dx) > 1.0f || fabs(dy) > 1.0f)
+          continue; // Ignore the point that is not stable
+
+        // Refine the coordinates
+        kp.pt.x += dx * ratio + .5f*(ratio-1.f);
+        kp.pt.y += dy * ratio + .5f*(ratio-1.f);
+
+        kp.angle = 0.0;
+        kp.size *= 2.0f; // In OpenCV the size of a keypoint is the diameter
+
+        // Push the refined keypoint to the final storage
+        output_keypoints.push_back(kp);
+      }
     }
   }
 }

modules/features2d/src/kaze/AKAZEFeatures.h

@@ -44,6 +44,7 @@ struct Evolution
   int sublevel;             ///< Image sublevel in each octave
   int sigma_size;           ///< Integer esigma. For computing the feature detector responses
   float octave_ratio;       ///< Scaling ratio of this octave. ratio = 2^octave
+  int border;               ///< Width of border where descriptors cannot be computed
 };
 
 /* ************************************************************************* */
@@ -76,8 +77,9 @@ public:
   void Create_Nonlinear_Scale_Space(InputArray img);
   void Feature_Detection(std::vector<cv::KeyPoint>& kpts);
   void Compute_Determinant_Hessian_Response(void);
-  void Find_Scale_Space_Extrema(std::vector<cv::KeyPoint>& kpts);
-  void Do_Subpixel_Refinement(std::vector<cv::KeyPoint>& kpts);
+  void Find_Scale_Space_Extrema(std::vector<Mat>& keypoints_by_layers);
+  void Do_Subpixel_Refinement(std::vector<Mat>& keypoints_by_layers,
+    std::vector<KeyPoint>& kpts);
 
   /// Feature description methods
   void Compute_Descriptors(std::vector<cv::KeyPoint>& kpts, OutputArray desc);

modules/features2d/test/test_detectors_invariance.cpp

@@ -230,10 +230,10 @@ INSTANTIATE_TEST_CASE_P(ORB, DetectorRotationInvariance,
                         Value(IMAGE_TSUKUBA, ORB::create(), 0.5f, 0.76f));
 
 INSTANTIATE_TEST_CASE_P(AKAZE, DetectorRotationInvariance,
-                        Value(IMAGE_TSUKUBA, AKAZE::create(), 0.5f, 0.76f));
+                        Value(IMAGE_TSUKUBA, AKAZE::create(), 0.5f, 0.71f));
 
 INSTANTIATE_TEST_CASE_P(AKAZE_DESCRIPTOR_KAZE, DetectorRotationInvariance,
-                        Value(IMAGE_TSUKUBA, AKAZE::create(AKAZE::DESCRIPTOR_KAZE), 0.5f, 0.76f));
+                        Value(IMAGE_TSUKUBA, AKAZE::create(AKAZE::DESCRIPTOR_KAZE), 0.5f, 0.71f));
 
 /*
  * Detector's scale invariance check