Image segmentation is the process of partitioning a digital image into multiple segments which makes the image more meaningful and easier to analyze. It is typically used to locate objects and boundaries (lines, curves, etc.) in images. Image Threholding is one of the Image segmentation methods, it converts the gray-scale image into a binary image.Variational minimax optimization is one of the best methods used for Image thresholding [5-9].In this paper I would study the the performance of this algorithm for a Noisy Gray scale image. For this, I consider an Image processing system model which is a logical block diagram of the processes involved in this performance study. The performance however will be in terms of Image similarity observed between the original binary image and the denoised but degraded binary image obtained using the above mentioned Image thresholding algorithm, The Image similarity or Image Quality is represented as Universal image quality index  which will differ for different values of SNR for the Noisy Gray scale Image. Finally the results are tabulated and conclusions are made.
In many applications of image processing, the gray levels of pixels belonging to the object or foreground are quite different from the gray levels of the pixels belonging to the background. Thresholding becomes then a simple tool to separate foreground from the background. Examples of thresholding applications are document image analysis where the goal is to extract printed characters logos, graphical map processing where lines, legends, characters are to be found, quality inspection of materials etc .The output of the thresholding operation is a binary image whose gray level of 0 (black) will indicate a pixel belonging to a print, legend, drawing, or target and a gray level of 1 (white) will indicate the background. Some input/output devices, such as laser printers, fax machines, and bi-level (0 and 1) computer displays, can only handle bi-level images. Because of the small size of the binary image files, fax machine and document management solutions usually use this format. The fundamental challenge in the field of image processing and computer vision is image noise. Image noise is random variation of brightness or colour information in images. It can be produced by the sensor and circuitry of a scanner, fax machine or digital camera. Image noise is an undesirable by-product of image capture that adds spurious and extraneous information. Image noises are of many types such as Gaussian noise, salt and pepper noise; shot noise, quantisation noise etc. I restrict my discussion to Gaussian noise; principal sources of Gaussian noise in digital images arise during acquisition . Hence, Image noise poses as a challenge to the performance of various image processing algorithms.
2. Image Processing System Model
Figure1. An Image Processing System Model
Image processing system model given ...