Owing to errors introduced during the process of segmentation and feature extraction, the matching of scene features with model features may not always be exact. Therefore, a certain amount of tolerance has to be incorporated into the process of matching a scene feature with a model feature. Tolerance in the matching process will cause an error in the computed pose parameters. During the course of experiments based on matching and pose computation using dihedral junctions, the computed pose parameters were found to be sensitive to the difference in the included angles of the model dihedral junction (θ m ) and the scene dihedral junction (θ s ) (Figure 8.1). The rotation parameters were found to be much more sensitive than the translation parameters. The objective of this chapter is to present a formal analysis of the sensitivity of the computed pose to the difference in the included angles of the model and scene dihedral junctions. Based on the sensitivity analysis, a fuzzy-probabilistic model of the generalized Hough transform is proposed. The proposed model provides an analytical explanation of how the use of qualitative features provides greater robustness for the generalized Hough transform. Although the analysis is done for the case of matching dihedral junctions or dihedral feature junctions, the approach taken in the sensitivity analysis is general and can be extended to matching based on other feature types.
KeywordsMembership Function Fuzzy Number Model Feature Qualitative Feature Included Angle
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