This paper describes the use of the radial transform about the principles and methods of feature extraction, the basic principle mainly from the Gareth Loy and Alexander Zelinsky A Fast Radial Symmetry Transform for Detecting Points of Interest article. Need the original can leave the mailbox.
Radial Symmetry Transform (radially symmetric transformation) is somewhat analogous to a circular Hough transform, the main difference between the two is: the former mainly on the role of each pixel in an image and its surrounding pixels in the neighborhood (contribution), while the latter mainly on the role of a pixel neighborhood of the current pixel (contribution). Algorithm complexity of the algorithm is O (KN), where K is the total number of pixels of the original image, N is the neighborhood range investigated of N * N.
The following briefly describes the basic idea of the algorithm, first define the orientation projection image On (direction projection view On) and magnitude projection image Mn (projection size)
Each pixel on the original image point p calculated gradient value G (p), n is set to transform the radius radially symmetric, then there will be a positively-a ff ected pixel P + ve (p each pixel at each point p ) and negatively-a ff ected pixel P-ve (p).
The figure shows two corresponding respectively to the center range n p is the radius of the circle, and the P + ve to G (p) pointed to the point, the P-ve to G (p) facing away from the point. Two corresponding calculated as follows:
On now consider how to establish and Mn:
On the upper respectively corresponding to P + ve and P-ve two points plus 1 and minus 1, respectively, and the points corresponding to the Mn were added thereto || g (p) ||, and || Save g (p ) ||, respectively, calculated as follows,
After all pixels in the original image is traversed also established corresponding image On and image Mn, radially symmetrical image after the conversion is calculated through the next, as follows:
n radius set forth above, Sn i.e. converted image obtained, wherein Fn as follows:
In the description that is the image matrix calculation method may be applied to each other like transformation. The above formula should not be difficult to understand. As for why he does it, the article did not explain, I belong to the rookie, not thinking interpretation of Daniel.
Namely, it can be obtained in substantially a radial symmetry through the image after conversion. Finally, i.e. a so-called full transform all symmetric conversion range n and the sum, as follows:
After a few transform paste FIG:
