II implemented a technique to extract intensity-based boundaries from images and match them to those extracted by other images.The technique is sensitive to orientation of the objects and can distinguish mirrored version of the same object. I focused on two papers:

Automatic Target Recognition by Matching Oriented Edge Pixels (1997)
Clark F. Olson, Daniel P. Huttenlocher, IEEE Transactions on Image Processing

A multi-resolution technique for comparing images using the hausdorff distance.
D. P. Huttenlocher and W.J. Rucklidge, Proceedings of the Conference on Computer Vision and Pattern Recogntion, pages 705--706, 1993

Details of the maths and the algorithms to calculate the result are given in the final report
[ Final report ]

Problem statement

The shape we want to match

should be located in a test image:

The image above shows the ground-truth. Green circles indicate the locations we want to find, the yellow and the red locations should be discarded, because they are not oriented correctly.

We need two transformations of the image for a fast implementation. The Distance Transform of the source image (for each pixel the distance to the boundary is computed)

and the angel transform (each pixel is assigned the orientation of the closest point on the boundary)

Results

All five instances of the object in the source image could be found. No object was located at yellow or red marked spots. The example images underneath show 2 of the 5 located instances:

Implementation details

Everything is written in C++, using the Intel Integrated Performance Primitives (IPP) 5.1 to compute the Canny Edge images, gradients and everything which works on a big amount of data, like the determination of the K-th largest element of a vector. Furthermore I use openCV to load and save images and to display the results on screen. The Intel Math Kernel library is also required for compilation, cause of the integration of my Matrix class, which I use to speed up the transformations.