Multilevel thresholding for image segmentation through a fast statistical recursive algorithm

Abstract

A novel algorithm is proposed for segmenting an image into multiple levels using its mean and variance. Starting from the extreme pixel values at both ends of the histogram plot, the algorithm is applied recursively on sub-ranges computed from the previous step, so as to find a threshold level and a new sub-range for the next step, until no significant improvement in image quality can be achieved. The method makes use of the fact that a number of distributions tend towards Dirac delta function, peaking at the mean, in the limiting condition of vanishing variance. The procedure naturally provides for variable size segmentation with bigger blocks near the extreme pixel values and finer divisions around the mean or other chosen value for better visualization. Experiments on a variety of images show that the new algorithm effectively segments the image in computationally very less time.

An Automatic Multilevel Image Thresholding Using Relative Entropy and Meta-Heuristic Algorithms

“…The first image, which has a known number of three thresholds as in this case is tested ( Figure 4a); secondly, an image containing text on a wrinkled paper which will cause lighting variation is tested (Figure 5a). Thirdly, the Lena image (Figure 6a) [1,[12][13][14][15] is tested, which is considered as a benchmark image when a new thresholding technique is proposed. …”

“…This should provide a good description of the observed probabilities p(i) given by the gray level histogram of the image under study. However, finding an appropriate number of distributions, i.e., "d", is a very difficult task [12][13][14][15]. Consequently, the addition of a new term in Equation (2), which is detailed in the following subsection helps to automatically determine a suitable amount of distributions.…”

Multi-level threshold based edge detector using logical operations

“…The proposed edge detection is performed in three stages: first the grayscale image with a resolution of 8 bits/pixel is down-sampled to multiple binary images (1 bit/pixel) for different threshold levels selected optimally using the algorithm specified in Arora et al (2008). Then, the binary images are circularly shifted left, right, up and down.…”

“…The threshold levels were selected optimally using the algorithm given in Arora et al (2008) and reproduced here for convenience. The free parameters α and β control the sub-range span to guarantee that the sub-range does not include more than one structure (object), or a single structure (object) does not broaden beyond a specific sub-range.…”

“…This averts the clustering of different objects within a small range. Moreover if the image has a skewed/asymmetric histogram, the free parameters can be adjusted to improve the quality of the down converted image without the added burden of computational complexity and time (Arora et al, 2008). For simplicity, the free parameters α and β are chosen to be 1.…”