Robust shape normalization based on implicit representations

Abstract

We introduce a new shape normalization method based on implicit shape representations. The proposed method is robust with respect to deformations and invariant to similarity transformations (translation, isotropic scaling and rotation). The new method has been tested and compared to the classical shape normalization method and previous work in terms of aligning groups of shapes with deformations.

Iterative Graph Cuts for Image Segmentation with a Nonlinear Statistical Shape Prior

“…U shape (Ω, Ω j ) separated log shape kernel density + const, (18) verifying that the inequality condition (Eq. 16) holds.…”

“…2 (See Appendix A for details on calculating these parameters). This method worked well for our examples; however, other shape alignment schemes may be used [1,18,20,30,33].…”

“…To improve performance, one may calculate the transformation needed for a single template, and use that transformation for the entire set of templates. One may also use a fast moment-based method [18,26] to provide an initial state for shape alignment.…”

“…where s j is the inertial scale of a shape Ω j as defined in Jiang and Tomasi [18]. Note that this expression of the shape prior is potentially multi-modal.…”