A Dynamically Masked Gaussian Can Efficiently Approximate a Distance Calculation for Image Segmentation

Abstract

One of the most commonly applied image filtering algorithms is the Gaussian blur. An image is convolved with the radially symmetric Gaussian kernel, and each pixel is replaced by a weighted average of all its surrounding neighbors. While this performs admirably for general smoothing of local intensity variation, it has no awareness of important structures within the image. Therefore, the smoothing is applied in an equal and unbiased manner. Unfortunately, for applications in which preservation of edges is required, the Gaussian blur is inadequate due to its indiscriminate nature. In this chapter, we present an algorithm for dynamically masking the Gaussian kernel to remove from consideration any pixels of undesirable intensity. This has the effect of allowing the Gaussian to discern and protect edges of any strength or width, as well as, given the radially symmetric nature of the kernel, approximating a distance function when the kernel is set to a domain-specific object size. The dynamic masking is precalculable and adds negligible processing time to the normal operation of Gaussian convolving, thus making it a highly useful preprocessing step for image segmentation applications.