Model based scale-space algorithms for object detection: experimentation and statistical analysis
V.A. Topkar · 1992
Scale-space representation is a powerful tool in computer vision and has been a topic of interest in the recent past. Scale-space representation of an image is obtained by convolving the image with a bank of smoothing filters, each tuned to a different resolution, and detecting the zero crossings (z.c.s) of the second derivatives of the outputs. The focus of the research in scale-space so far has been on coarse-to-fine focusing methods, image reconstruction, and computational aspects. However, not much work has been done on the signal detection problem, i.e. detecting the presence or absence of signal models from a given scale-space representation. In this dissertation we propose four model-based object detection algorithms for separating the objects from the background in the scale-space domain. These algorithms do not need any thresholding at any of the scales. The different algorithms are applicable to images with different noise and clutter characteristics. The algorithms are demonstrated on several real life images. One of the major problems in scale-space, as in any other approach, is the presence of noise and clutter. The problem is more pronounced in scale-space because it involves higher derivatives of the noise. Statistical analysis of the noise as it is reflected in the scale-space representation and its effect on any algorithm based on it poses an interesting topic of research. Statistical analysis of the scale-space is nontrivial because of two reasons: (i) it involves a nonlinear operation, namely the detection of zero crossings and (ii) the noise at different scales is correlated. In the second part of this dissertation we prove theorems which give the probabilities of zero-crossings in the output in the presence of noise. The theorems are then applied to the case of Gaussian smoothing. These probabilities can be used for a number of applications such as optimum filter design, performance analysis and active multiscaling. It is hoped that the statistical analysis of scale-space will provide an analytical framework to answer questions such as how many & which scales should be used, which smoothing filters will perform better, how does the power & the spread of the input noise affect the scale-space representation etc.