yes / Canny (IEEE Trans. Pattern Anal. Image Proc. 8(6):679-698, 1986) suggested that an optimal edge detector should maximize both signal-to-noise ratio and localization, and he derived mathematical expressions for these criteria. Based on these criteria, he claimed that the optimal step edge detector was similar to a derivative of a gaussian. However, Canny's work suffers from two problems. First, his derivation of localization criterion is incorrect. Here we provide a more accurate localization criterion and derive the optimal detector from it. Second, and more seriously, the Canny criteria yield an infinitely wide optimal edge detector. The width of the optimal detector can however be limited by considering the effect of the neighbouring edges in the image. If we do so, we find that the optimal step edge detector, according to the Canny criteria, is the derivative of an ISEF filter, proposed by Shen and Castan (Graph. Models Image Proc. 54:112-133, 1992). In addition, if we also consider detecting blurred (or non-sharp) gaussian edges of different widths, we find that the optimal blurred-edge detector is the above optimal step edge detector convolved with a gaussian. This implies that edge detection must be performed at multiple scales to cover all the blur widths in the image. We derive a simple scale selection procedure for edge detection, and demonstrate it in one and two dimensions.

This work deals with methods of segmentation of biomedical image signals. It describes, sums up and compares representative methods of digital image processing. Segmentation based on parametric representation is one of the mentioned methods. So as the basic parameter can be chosen for example luminance and the final binary image is obtained by thresholding. Next described method is segmentation based on edge representation. This method can be divided into edge detection by the help of edge detectors and of Hough transformation. Edge detectors work with the first and second derivation. The following method is region-based segmentation, which can be used for a image with noise. This category can be divided into three parts. The first one is segmentation via splitting and merging regions, when the image is split and the created regions are tested on a defined condition. If the condition is satisfied, the region merges and doesn’t continue splitting. The second one is region growing segmentation, when adjacent pixels with a similar intensity of luminance are grouped together and create a segmentated region. Third one is watershed segmentation algorithm based on the idea of water diffusion on uneven surface. The last group of methods is segmentation via flexible and active contours. Here is described an active shape model proceeding from a possibility to deform models so that they match with sample shapes. Next I also describe method Snakes, where occurs gradual contour shaping up to the edge of the object in the image. For the final editing is used mathematical morphology of segmentated images. I aimed to meet methods of image signals segmentation, to cover the chosen methods as a script in programming language Matlab and to check their properties on images.

This thesis presents the Deriche edge detector as an interesting alternative to the commonly used edge detectors. The Deriche edge detector's design is presented to the reader as well as its strengths and weaknesses. Performance issues of the Deriche edge detector are described in comparison with the Canny edge detector together with recommendations for using the Deriche detector. Finally, edge detection quality of the Deriche edge detector is compared to the Canny edge detector using robust subjective evaluation method.