Adaptive tensor-based morphological filtering and analysis of 3D profile data

Abstract: Image analysis methods for processing 3D profile data have been investigated and developed. These methods include; Image reconstruction by prioritized incremental normalized convolution, morphology-based crack detection for steel slabs, and adaptive morphology based on the local structure tensor. The methods have been applied to a number of industrial applications.An issue with 3D profile data captured by laser triangulation is occlusion, which occurs when the line-of-sight between the projected laser light and the camera sensor is obstructed. To overcome this problem, interpolation of missing surface in rock piles has been investigated and a novel interpolation method for filling in missing pixel values iteratively from the edges of the reliable data, using normalized convolution, has been developed.3D profile data of the steel surface has been used to detect longitudinal cracks in casted steel slabs. Segmentation of the data is done using mathematical morphology, and the resulting connected regions are assigned a crack probability estimate based on a statistic logistic regression model. More specifically, the morphological filtering locates trenches in the data, excludes scale regions for further analysis, and finally links crack segments together in order to obtain a segmented region which receives a crack probability based on its depth and length.Also suggested is a novel method for adaptive mathematical morphology intended to improve crack segment linking, i.e. for bridging gaps in the crack signature in order to increase the length of potential crack segments. Standard morphology operations rely on a predefined structuring element which is repeatedly used for each pixel in the image. The outline of a crack, however, can range from a straight line to a zig-zag pattern. A more adaptive method for linking regions with a large enough estimated crack depth would therefore be beneficial. More advanced morphological approaches, such as morphological amoebas and path openings, adapt better to curvature in the image. For our purpose, however, we investigate how the local structure tensor can be used to adaptively assign to each pixel an elliptical structuring element based on the local orientation within the image. The information from the local structure tensor directly defines the shape of the elliptical structuring element, and the resulting morphological filtering successfully enhances crack signatures in the data.