Abstract
Extrinsic factors such as object pose and camera parameters are a main source of shape variability and pose an obstacle to efficiently solving shape matching and inference. Most existing methods address the influence of extrinsic factors by decomposing the transformation of the source shape (model) into two parts: one corresponding to the extrinsic factors and the other accounting for intra-class variability and noise, which are solved in a successive or alternating manner. In this chapter, we consider a methodology to circumvent the influence of extrinsic factors by exploiting shape properties that are invariant to them. Based on higher-order graph-based models, we implement such a methodology to address various important vision problems, such as non-rigid 3D surface matching and knowledge-based 3D segmentation, in a one-shot optimization scheme. Experimental results demonstrate the superior performance and potential of this type of approach.
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- 1.
The shape can also be associated with a texture model if photometric information is available.
- 2.
When a bijective mapping between S 1⊂R 3 and S 2⊂R 3 is required, the feasible solution can be defined as all diffeomorphisms that map S 1 to S 2.
- 3.
Photometric variation can be caused by the change of illumination. We mostly focus on the geometric aspect here but the extension to the photometric aspect can be done analogously.
- 4.
The definition of the intrinsically equivalence depends on the problem to be addressed. For instance, when dealing with nonrigid 3D surface matching, we often assume that two surfaces differing by an isometric transformation (with geodesic metrics) are intrinsically equivalent.
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Wang, C., Zeng, Y., Samaras, D., Paragios, N. (2013). Modeling Shapes with Higher-Order Graphs: Methodology and Applications. In: Dickinson, S., Pizlo, Z. (eds) Shape Perception in Human and Computer Vision. Advances in Computer Vision and Pattern Recognition. Springer, London. https://doi.org/10.1007/978-1-4471-5195-1_31
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DOI: https://doi.org/10.1007/978-1-4471-5195-1_31
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