Bi-level Thresholding Research Articles

Unimodal thresholding

Most thresholding algorithms have difficulties processing images with unimodal distributions. In this paper an algorithm, based on finding a corner in the histogram plot, is proposed that is capable of performing bilevel thresholding of such images. Its effectiveness is demonstrated on synthetic data as well as a variety of real data, showing its successful application to edges, corners, difference images, optic flow, texture difference images, polygonal approximation of curves, and image segmentation.

A fast scheme for optimal thresholding using genetic algorithms

Traditional optimal thresholding methods are very popular and efficient in the case of bi-level thresholding. But they are very computationally expensive when extended to multilevel thresholding since they exhaustively search the optimal thresholds to optimize the objective functions. In this paper, a fast scheme using genetic algorithms is proposed to render these optimal thresholding techniques more practical. The experimental results show that the proposed scheme can make the optimal thresholding methods applicable in the case of multilevel thresholding and the performances are better than those of some property-based multilevel thresholding methods.

A fast iterative scheme for multilevel thresholding methods

The previously published optimal thresholding techniques based on some objective functions are very efficient in the bi-level thresholding case, but they are impractical when extended to multilevel thresholding. The reason for this is their computational complexity which grows exponentially with the number of thresholds. In this paper, an iterative scheme is proposed to render these optimal thresholding techniques more practical. The proposed algorithm starts with a bi-level thresholding, then uses the initial results to obtain higher-order thresholds. This algorithm is iterative and the convergence is proved. We also introduce some useful programming techniques to make the computation more efficient. The proposed algorithm can therefore determine the number of thresholds automatically as well as save a significant amount of computing time.

A new criterion for automatic multilevel thresholding

A new criterion for multilevel thresholding is proposed. The criterion is based on the consideration of two factors. The first one is the discrepancy between the thresholded and original images and the second one is the number of bits required to represent the thresholded image. Based on a new maximum correlation criterion for bilevel thresholding, the discrepancy is defined and then a cost function that takes both factors into account is proposed for multilevel thresholding. By minimizing the cost function, the classification number that the gray-levels should be classified and the threshold values can be determined automatically. In addition, the cost function is proven to possess a unique minimum under very mild conditions. Computational analyses indicate that the number of required mathematical operations in the implementation of our algorithm is much less than that of maximum entropy criterion. Finally, simulation results are included to demonstrate their effectiveness.

Automatic thresholding based on human visual perception

An automatic thresholding method based on aspects of the human visual system which preserved edge structure in images is proposed. We first determine edge thresholds based on human visual perception, and then use these edge thresholds to find several edge intervals. From these edge intervals, we find the threshold value(s) at which most edge information is preserved in the thresholded image. A bilevel thresholding algorithm is first described, and then two multilevel thresholding algorithms called Nm-multilevel thresholding and mN-multistep thresholding are derived through a slight modification of the bilevel thresholding algorithm. The multistcp thresholding algorithm directly uses bilevel thresholding sequentially to select m threshold values one by one so as to speed up the thresholding process. The proposed thresholding method is simple, requiring neither an iterative operation nor edge detection.

Moment preserving detection of elliptical shapes in gray-scale images

A new method for elliptical shape detection based on the principle of gray and mass moment preserving is proposed. For each elliptical region in a gray-scale image, automatic bilevel thresholding based on gray moment preserving is used first to transform the blurred image in the region into a binary picture. The five parameters of the elliptical shape are then computed using the mass moment preserving principle. A major merit of the method is that these parameters can be uniquely and analytically determined without iterative computation. By the proposed method, other shapes like rectangles, circles, semi-circle running tracks, etc. can also be detected. Experimental results show the effectiveness of the proposed method.

Moment-preserving corner detection

A new corner detection method based on the principle of preserving gray and mass moments is proposed. For each circular region in a digital image, bilevel thresholding based on gray moment preserving is used first to transform the blurred subimage in the region into a binary picture. Two approximate boundary points on the circumference of the thresholded circular region are obtained next by simple traversal. An approximate corner point is estimated from the geometric relation between the centroid and the three vertices of the triangular lamina formed by the corner pattern within the circular region. These points are then used as an initial guess for solving a system of nonlinear equations that are constructed by preserving the area and the three mass moments of the partial object lamina within the circular region. More accurate corner boundary points can finally be determined, from which not only the location but also the orientation as well as the angle of the corner can be computed. Experimental results show the effectiveness of the proposed method.