Shape statistics in kernel space for variational image segmentation. (English) Zbl 1035.68125
Summary: We present a variational integration of nonlinear shape statistics into a Mumford–Shah based segmentation process. The nonlinear statistics are derived from a set of training silhouettes by a novel method of density estimation which can be considered as an extension of kernel PCA to a probabilistic framework.
We assume that the training data forms a Gaussian distribution after a nonlinear mapping to a higher-dimensional feature space. Due to the strong nonlinearity, the corresponding density estimate in the original space is highly non-Gaussian.
Applications of the nonlinear shape statistics in segmentation and tracking of 2D and 3D objects demonstrate that the segmentation process can incorporate knowledge on a large variety of complex real-world shapes. It makes the segmentation process robust against misleading information due to noise, clutter and occlusion.
We assume that the training data forms a Gaussian distribution after a nonlinear mapping to a higher-dimensional feature space. Due to the strong nonlinearity, the corresponding density estimate in the original space is highly non-Gaussian.
Applications of the nonlinear shape statistics in segmentation and tracking of 2D and 3D objects demonstrate that the segmentation process can incorporate knowledge on a large variety of complex real-world shapes. It makes the segmentation process robust against misleading information due to noise, clutter and occlusion.
MSC:
| 68U10 | Computing methodologies for image processing |
Keywords:
Probabilistic kernel PCA; Nonlinear shape statistics; Density estimation; Image; segmentation; Variational methods; Diffusion snakesReferences:
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