Optical edge defection based image segementation algorithms

Abstract

The work reported in this thesis primarily addresses edge detection algorithms in noisy images. The subjective errors that are inevitable in preprocessing and postprocessing generally used in edge detection cause errors in final segmentation. The objective of the present work is to eliminate these subjective errors and to obtain global edges that are thin and spatially contiguous, thereby requiring minimal postprocessing. Of the two approaches to edge detection—sequential and parallel—the latter has become quite popular due to its inherent advantages. In parallel edge detection, the image is convolved with a local edge operator. The edge operator responds strongly in the presence of edges and weakly otherwise. A threshold setting on the response of an edge operator yields a binary edge picture. A global threshold on the response of an edge operator is not adequate in the presence of noise. In noisy images, the response of a local edge operator may be strong where there is no edge or weak where there is one. Thus, there is no one-to-one correspondence between edge presence and operator response. Many methods, such as variable size operators, have been proposed to circumvent the problems arising from noise. This thesis proposes a new edge detection scheme using a variable (adaptive) local threshold based on local image properties in a 3×3 window. The local threshold is modeled as a nonlinear function of the edge operator’s responses at all points in the neighborhood. The threshold is controlled by two parameters, which depend on the gradient amplitude distributions of edge and no-edge pixels. These parameters can be estimated from training data sets or interactively if training data is unavailable.

Low contrast edges can be detected by increasing one parameter. The other parameter helps eliminate isolated and parallel edges by increasing the threshold for pixels lacking neighborhood support.

The algorithm is described in detail and demonstrated on a computer-generated image with vertical and horizontal step edges at different contrast levels. Zero-mean Gaussian noise is added at two levels to evaluate performance. Results are compared with global threshold techniques using real-world datasets including:

Landsat image House scene Chromosome image Blood cell image

The interactive algorithm requires knowledge of the image. An automatic method for estimating optimal threshold parameters involves numerically characterizing the edge map. The proposed figure of merit (FOM) is a weighted combination of thinness and connectedness of edges in a 3×3 window, summed over the entire edge map. The threshold parameters are estimated by maximizing FOM, yielding the optimal edge map. The Nelder-Mead simplex search algorithm is used for optimization. The algorithm is tested on computer-generated images at different noise levels and compared with optimal global threshold techniques. Using Roberts and Sobel operators, the algorithm shows promising results across various images. Additionally, a clustering algorithm is proposed for edge detection in noisy images. Pixels are clustered into edge and no-edge classes in a 2D feature space using:

Edge strength (operator response) Edge evidence (heuristic feature in a 3×3 window)

Edge evidence is controlled by two parameters. Tuning these parameters yields thin and spatially contiguous edges. The algorithm works interactively, and results are presented for various image datasets. The parameters of edge evidence can also be estimated automatically by maximizing FOM. Initially, clusters are formed in feature space for some parameter values. Cluster members are mapped onto the image plane and FOM is computed. This is done iteratively using the Nelder-Mead simplex method until FOM is maximized. The resulting edge map is the optimal edge map for the given image. The results demonstrate the potential applications of this approach to edge detection.