Merge pull request opencv#17907 from Yosshi999:gsoc_asift-py2cpp

* Implement ASIFT in C++

* '>>' should be '> >' within a nested template

* add a sample for asift usage

* bugfix empty keypoints cause crash

* simpler initialization for mask

* suppress the number of lines

* correct tex document

* type casting

* add descriptorsize for asift

* smaller testdata for asift

* more smaller test data

* add OpenCV short license header

Author: Yosshi999

doc/opencv.bib

@@ -584,6 +584,16 @@ @inproceedings{Kolmogorov03
   pages = {1033--1040},
   publisher = {IEEE}
 }
+@article{YM11,
+  author = {Yu, Guoshen and Morel, Jean-Michel},
+  title = {ASIFT: An Algorithm for Fully Affine Invariant Comparison},
+  year = {2011},
+  pages = {11--38},
+  journal = {Image Processing On Line},
+  volume = {1},
+  doi = {10.5201/ipol.2011.my-asift},
+  url = {http://www.ipol.im/pub/algo/my_affine_sift/}
+}
 @inproceedings{LCS11,
   author = {Leutenegger, Stefan and Chli, Margarita and Siegwart, Roland Yves},
   title = {BRISK: Binary robust invariant scalable keypoints},

modules/features2d/include/opencv2/features2d.hpp

@@ -245,6 +245,31 @@ typedef Feature2D DescriptorExtractor;
 //! @{
 
 
+/** @brief Class for implementing the wrapper which makes detectors and extractors to be affine invariant,
+described as ASIFT in @cite YM11 .
+*/
+class CV_EXPORTS_W AffineFeature : public Feature2D
+{
+public:
+    /**
+    @param backend The detector/extractor you want to use as backend.
+    @param maxTilt The highest power index of tilt factor. 5 is used in the paper as tilt sampling range n.
+    @param minTilt The lowest power index of tilt factor. 0 is used in the paper.
+    @param tiltStep Tilt sampling step \f$\delta_t\f$ in Algorithm 1 in the paper.
+    @param rotateStepBase Rotation sampling step factor b in Algorithm 1 in the paper.
+    */
+    CV_WRAP static Ptr<AffineFeature> create(const Ptr<Feature2D>& backend,
+        int maxTilt = 5, int minTilt = 0, float tiltStep = 1.4142135623730951f, float rotateStepBase = 72);
+
+    CV_WRAP virtual void setViewParams(const std::vector<float>& tilts, const std::vector<float>& rolls) = 0;
+    CV_WRAP virtual void getViewParams(std::vector<float>& tilts, std::vector<float>& rolls) const = 0;
+    CV_WRAP virtual String getDefaultName() const CV_OVERRIDE;
+};
+
+typedef AffineFeature AffineFeatureDetector;
+typedef AffineFeature AffineDescriptorExtractor;
+
+
 /** @brief Class for extracting keypoints and computing descriptors using the Scale Invariant Feature Transform
 (SIFT) algorithm by D. Lowe @cite Lowe04 .
 */