Size-sensitive multiresolution decomposition of images with rank order based filters

Abstract

In this paper, the problem of size-sensitive multiresolution decomposition is addressed. It is shown that various decompositions can be achieved using a class of nonlinear filters known as rank order based filters. This class includes, as a special case, classical rank order filters and a large number of morphological filters with flat structuring element. As the notion of size in an image is related to shape, two kinds of decomposition are investigated. In the first one, the object size is assessed by comparison with a set of arbitrary masks (squares) and does not take into account the actual shape of the objects present in the image. This approach leads to a nonadaptive size-sensitive decomposition. In the case of texture images, this nonadaptive decomposition can be attractively replaced by an adaptive scheme. This last approach consists in extracting a set of dominant shapes of given sizes contained in the image and in assessing the size of a specific element by comparison with the various dominant shapes. In both cases, particular attention is paid to the problem of shape preservation in the hierarchy. It is concluded that in the case of nonadaptive decomposition, the shape is far from being preserved. To address this problem, a specific but simple processing step is proposed. It is based on modification and combination of geodesic erosion and dilation. This approach is attractive because of its simplicity and of the very good shape preservation it allows. As applications, multiresolution decomposition is applied to defect detection and grey level segmentation problems. In the case of defect detection, multiresolution decomposition is used as a simplification tool which retains the image components of useful size. A large number of grey level and texture defect detections are described to show the robustness and accuracy of the approach. Decomposition can also be used as a starting point of a grey level segmentation algorithm. Examples of very simple segmentation techniques are described and discussed.