An image filter algorithm using level set based on discontinuous PDE

Abstract

An image filter based on nonlinear discontinuous partial differential equation (PDE) is presented. It models a class of morphological image filters called the level set method for gray image processing. We discuss the theoretical aspects of this PDE. The switch signal is controlled by the discontinuous right hand of PDE. We propose a discrete algorithm for its numerical solution and corresponding filter implementation. The study provides insights via several experiments. These types of filters are very useful in numerical image analyses.The preliminary filtering step is necessary for segmenting an image into a meaningful partition, in order to suppress noise and small meaningless details and textures. Morphological segmentation is mainly based on detecting the edges of a gradient image. However, gradient operators are very sensitive to noise and textured areas. Hence, the image has to be smoothed before segmentation. The linear smoothing will blur the outline and smooth across the object boundaries. Therefore, the nonlinear smoothing technologies have been proposed [1] . A lot of smoothing simplifies the detection but proves to be less effective in localizing contours; little smoothing, however, does not suppress enough noise.In computer vision, the continuous models have been proposed for scale-space image analysis based on partial differential equations (PDEs). Using an intuitive mathematical model of PDEs can simulate its physical characteristic better. It can achieve the sub-pixel precision. These continuous questions are often solved by linear method. The linear smoothing will shift and fuzzy the boundary of images, but nonlinear smoothing can decrease or avoid these influences completely. The corrosion operation, the dilation operation and the medians filter operation do well in protecting the vertical image edges, but make the horizontal image edges shift and fuzzy. The opening/closing operation given later is a kind of stronger filter. They are composed of a reference signal f that contains several parts and a marked signal g (initial seed) that holds in the parts of the signal f. They can reconstruct the entire object and protect the boundary and the edge.