Application of generalized method of least modules in problems of processing and analysing images

The article describes the use of nonlinear smoothing filter for image processing and analysis. Description of the model of the smoothing filter based on the generalized method of the least absolute values is given. The filter constructed on the basis of the offered model efficiently reduces the noise on brightness difference. Along with noise reduction in the contrast images, this method can be used for the solving problems of machine vision, medical diagnostics, etc. It has been found that nonlinear filtration on the basis of the generalized method of the least modules allows to solve such problems as clarification of the boundaries of contrast objects and segmentation of the image. There has been shown the possibility of recovering the boundaries of the images in which the contrast borders were blurry. X-ray image of an animal hand with defocusing was used as an example. After filtering, the contrast boundary was restored to the place where it was originally located. When processing a fluorography image, the filter removed various artifacts from the image and increased the contrast. Removal of artifacts along with the recoveries of the boundaries of contrast objects improves the overall “readability” of the fluorography image and also allows seeing earlier not distinguishable details on the image. Examples of the filter application in the clustering problem using the k-means algorithm are given. Due to the lack of this algorithm, applying it directly to the image does not give an acceptable result. However, after processing the original image with a nonlinear filter, the application of the k-means algorithm yields the desired result.