A Statistical Framework for Detection of Connected Features

This document provides a general idea of what edge-detection is and how it works, Eg., for Computer vision etc., Edge detectors are often operated with arbitrary parameters such as thresholds. Determining the significant values for these parameters on a trial and error basis may be a problem. It is therefore beneficial to try to understand edge-detection in terms of established quantitative methods. Here we show how the idea of an Hypothesis test can be used for significance testing and that provided there is the same null hypothesis distribution everywhere in an image, applying Hypothesis testing is the same as thresholding. We show how the method of error propagation can be used to find out if we have uniform noise on a feature enhancement. We apply this analysis to the Canny algorithm for detection of step edges. We explain that for other than step edges this algorithm needs modification and how this can be done while staying within the overall framework for the detection of connected features via non-maximal suppression and hysteresis thresholding. The DoG is a linear filter which has the required properties for algorithmic stability, and can be used for the detection of ridge structures. The orientation of the ridge is defined for this process as the direction of maximum second derivative. This ridge detector is then evaluated for the task of fly wing analysis, by looking at the specific characteristics of noise and scale stability. Background Edges are image attributes that are useful in image analysis and classification. The edge is widely defined to be an abrupt change of grey level values and its location is identified as the midpoint of the edge slope [1]. The sharp changes in intensity are important as they correspond to illumination changes such as shadows and illumination gradients or changes in orientation, distance from the viewer or surface reflectance, material, or to object boundaries [2]. Edges can also be perceived in regions with different optical characteristics such as contrast, colour and texture. The subjective approach of edge definition and characterisation and its wide range of applications have given rise to the development of large number of edge detectors that vary in performance [1]. Edge detection plays a significant role in object recognition and shape analysis. It simplifies image processing & analysis by drastically reducing the volume of the data to be processed whilst preserving useful and important structural information in the image. Essential information in the image is preserved in the edge map of the image and edge structures have an apparent relevance in the biological systems according to Marr [2]. Vernon [3] states that an image comprised of boundaries alone is a higher-level representation of the scene than the original grey level image. Moreover, edge information in an image tends to be robust to a certain extent under varying illumination or related camera parameters. Edge structures are considered primitive features and used widely in computational vision in areas such as scene segmentation, motion detection etc., There is an assumption that the edges detected have some physical significance [4]. The theoretical basis for the concept of an edge is best described by the mathematical concept of “diffeomorphic equivalence”. The basic idea is that, as the process of image formation can be described by a continuous function (eg; an optical model) of the underlying scene structure, differential discontinuities in the scene are preserved in the image. The extracted boundaries are useful in defining the location and shape of the features in the image. Object recognition becomes highly feasible if the boundary of an object can be traced successfully [5]. One major consideration of the behaviour of any feature detection algorithm is how well it performs in the presence of noise. In particular, is it capable of extracting the required image features for a wide range of images. Edge detection is conventionally carried out after filtering the image using a filter optimised for particular characteristics. These often aid in filtering the noise, however, this will also blur the edges since edges mostly comprise high spatial frequencies [5]. Edge Detection Algorithms Most of the edge detection algorithms involves the following few steps: • The image is convolved with a feature enhancement mask (for step edge detection this may be a gradient calculation). • The pixel positions with enhanced response greater than certain threshold level are labelled as feature tokens. This eliminates features that are most likely caused by noise. • For connected feature structures, linking is performed to ensure edge continuity by bridging the gaps of the isolated fragmented edges.