Computational Complexity Analysis of the Graph Extraction Algorithm for 3D Segmentation

The problem of partitioning images into homogenous regions or semantic entities is a basic problem for identifying relevant objects. Visual segmentation is related to some semantic concepts because certain parts of a scene are pre-attentively distinctive and have a greater significance than other parts. Unfortunately there are huge of papers for 2D images and segmentation methods and most graph-based for 2D images and few papers for spatial segmentation methods. We attempt to search a certain structures in the associated edge weighted spatial graph constructed on the image voxels, such as minimum spanning tree. The major concept used in graph-based 3D clustering algorithms is the concept of homogeneity of regions. For color 3D segmentation algorithms the homogeneity of regions is color-based, and thus the edge weights are based on color distance. Early graph-based methods use fixed thresholds and local measures in finding a 3D segmentation. Complex grouping phenomena can emerge from simple computation on these local cues. A number of approaches to segmentation are based on finding compact clusters in some feature space. A recent technique using feature space clustering first transforms the data by smoothing it in a way that preserves boundaries between regions. Our previous works are related to other works in the sense of pair-wise comparison of region similarity. In this paper we extend our previous work by adding a new step in the spatial segmentation algorithm that allows us to determine regions closer to it. We use different measures for internal contrast of a connected component and for external contrast between two connected components than the measures. The key to the whole algorithm of spatial segmentation is the honeycomb. The preprocessing module is used mainly to blur the initial RGB spatial image in order to reduce the image noise by applying a 3D Gaussian kernel. Then the segmentation module creates virtual cells of prisms with tree-hexagonal structure defined on the set of the image voxels of the input spatial image and a spatial triangular grid graph having tree-hexagons as cells of vertices.