Image decomposition by using the Hough transform with cubic B-spline curve

In this dissertation, various algorithms based on the Hough transform with cubic B-spline curves (HTCB) are developed for a variety of image processing applications, such as line or edge detection, curve-enclosed object detection.; First, an algorithm is presented using the Hough transform method for image decomposition into and description by curves representing image elements. The curves used for this representation are the periodic cubic B-spline curves. The image curves so represented can then be efficiently stored, resulting in a concise description of the objects' shapes. Other computation advantages, important among which is a small quantization error, are shown to be associated with the new algorithm. The new approach takes advantage of the well-known properties of the uniform cubic B-spline curves that changes in the coordinates of any vertex will only affect three segments in the immediate vicinity of the changed vertex. The general idea underlying this algorithm is to fit a B-spline to the curve and find the control vertices from Hough space (parametric space). This process is followed by the de Boor algorithm and a subdivision algorithm which can be used to reconstruct the detected curve.; Two algorithms based on the image decomposition by the Hough transform with cubic B-spline curves (IDHTCB) are proposed for circle and ellipse object detection. We pre-process the noisy images by using edge detection schemes such as gradient detectors, homogeneous detectors, etc. After edge detection of the input image, we remove the noise and extract the corresponding straight lines (symmetric horizontal and vertical lines) of the object by using the IDHTCB algorithm. These symmetric horizontal and vertical lines will give us the location of the objects. The curve-enclosed object is then reconstructed by using the properties of the object or the inversion formula (de Boor algorithm or subdivision algorithm).; Finally, the restoration approaches based on the IDHTUCB Algorithm with median filter (IDHTUCBMF) is proposed for improving both spatial degradation and point degradation. It yields excellent results in restoring the image as compared to the median filter and the average filter.