The aim of this research is extracting characteristics of the shapes of object images and removing noises on the images with preserving the characteristics. It is "pattern spectrum," which is an application of the mathematical morphology, a kind of nonlinear image operations, that is used to extract the characteristics. The pattern spectrum at first specifies a simple shape (called structuring element), and repeatedly applies the opening, which is a morphological operations to remove only image objects' portion that is completely included in the structuring element, on the image with similarly increasing the size of the structuring element of a fixed shape. This operation extracts how much area is occupied by the objects of each size.
This research modifies the patterns spectrum and defines the MOCS (Morphological Opening/Closing Spectrum) that extracts "the area of the portion that are smaller than a brush when the image is painted by this brush" for each size of brushes. The optimization of filters is realized by regarding the area that requires very sharp brush to be painted and modifying the parameters of filters to make the MOCS of filtered image similar to that of the original image except that the spectrum for very small size is removed on the filtered one. This method enables unsupervised filter optimization that requires no example of the ideal output, unlike the supervised optimization methods using artificial neural networks.
Example: a noisy image (left), the output of an unoptimized filter (center), the output of the optimized filter by this method (right).
Unsupervised filter optimization.