Hierarchical 3D diffusion wavelet shape priors

Abstract

In

Left Ventricle Segmentation Using Diffusion Wavelets and Boosting

“…The structure is encoded in a diffusion operator Δ ∈ R m×m . Combining those two diffusion approaches leads us to a prior knowledge of global and local training population variation [8]. The diffusion operator Δ is built on the set of points embedded in a metric space utilizing their mutual distance in the mean shape, and reflects all pairwise relations between individual points in the shape set.…”

“…The topology is learned from the training data instead of using a priori choices like e.g., a sphere and represents the shape variation by means of diffusion wavelets [7]. A detailed explanation of diffusion wavelet shape models, including variants of the parameterization can be found in [8].…”

“…The shape representation is based on a finite set of landmarks, that can be repeatedly identified and exhibit significant differentiation to the background on different examples of the anatomical structure, and more particularly for CT cardiac volumes. During the search the hierarchical diffusion wavelet shape model [8] is fitted to new data based on local appearance captured by the classifier. Related approaches combining local features with standard shape models are [10], or [11].…”

Local Shape Representation in 3D: from Weighted Spherical Harmonics to Spherical Wavelet

“…Dramatic changes in the wavelet coefficients can be caused by translating an image by even one pixel [13]. More recently in [27] the diffusion wavelet was used for shape representation, which requires training data and a set of landmarks. By using overcomplete SW [14,15], the aliasing problem can be overcome provided there is sufficient sampling at each scale.…”

Manifold-enhanced Segmentation through Random Walks on Linear Subspace Priors

“…In [4], prior knowledge on the shape of one muscle is further enforced by imposing the model to reside in a hierarchical shape space built via diffusion wavelets decomposition on training examples. Relying on iterative local optimization procedures, deformable models are very sensitive to the proximity of the initialization state with the expected solution, and usually only yield non-global optima of the objective function.…”