Computer Vision News - December 2016

The Original Hough Transform was developed to detect analytical shapes (lines, circles, ellipses, etc.). It does so by seeking the parameters defining the analytical representation of the shape obtained as local maxima in a so-called accumulator space (or Hough space). The GHT (Generalized Hough Transform) is an extension of the original Hough transform, introduced by Dana H. Ballard in 1981 , to enable detection of arbitrary shapes (i.e. those shapes that cannot be represented parametrically). The Matlab code we tried for you for the generalized Hough transform can be downloaded here . To generalize the Hough algorithm to non-analytic shapes, Ballard constructs the following: given any shape image and a pre-define reference point inside it, instead of a parametric curve in the transform stage, the information provided by the boundary pixels is stored in the form of the R-table (to be described in the next section). For object localization, every edge point on the test image is looked upon the R-table, the properties of the point are retrieved and the appropriate cell in a matrix called the Accumulator matrix is incremented. Next, we will examine code snippets of those two key elements of the GHT: Building the R- table and Object localization . Then, we will demonstrate how the GHT localizes an object in a given image. Building the R-Table Each entry of the R-table is comprised of two values: the gradient direction and all the boundary points corresponding to that gradient. The table is constructed as follows: given a reference point ( Xc , Yc ) inside the shape’s boundary (previously detected using an edge detector), the gradient direction – ɸ and the distance from the reference point – r (see image below) are computed for each boundary point (X,Y). The r values of each boundary point, indexed as a function of ɸ, constitute the R-table. Note that each index of ɸ may have many values of r . 10 Computer Vision News We Tried for You The Generalized Hough Transform Tried for You