Combining Point Distribution Models with Shape Models Based on Finite Element Analysis

Abstract

This paper describes a method of combining two approaches to modelling flexible objects. Modal Analysis using Finite Element Methods (FEMs) generates a set of vibrational modes for a single shape. Point Distribution Models (PDMs) generate a statistical model of shape and shape variation from a set of example shapes. A new approach is described which generates vibrational modes when few example shapes are available and changes smoothly to using more statistical modes of variation when a large data set is presented. Results are given for both synthetic and real examples. Experiments using the models for image search show that the combined version performs better than either the PDM or FEM models alone.

Segmentation of Cells with Partial Occlusion and Part Configuration Constraint Using Evolutionary Computation

“…When no clear geometrical representation exists, we model a shape (e.g. i th region's shape) by its statistical (from m training samples) and vibrational properties as X i ≈X i + S c i b i , whereX i is the average of a set of pose-normalized training shapes and S c i = S stat + βS vib is the combined (statistical S stat and vibrational S vib ) covariance matrix [8,4], β ∝ 1/m is the balancing parameter and…”

Physically And Statistically Based Deformable Models For Medical Image Analysis

“…Equation (33) by itself is insufficient to calculate (u, v); hence a second constraint, the velocity field smoothness constraint, is introduced. The velocity field can now be calculated as that which best satisfies both constraints by minimizing the following square error function:…”

“…A potential remedy is to present the snake with a priori information about the typical shape of the LV. Statistical knowledge about shape variation can be obtained using PDMs, which are central to the ASMs segmentation technique [33]. PDMs, which are obtained by performing PCA on landmark coordinates labeled on many example images, have been applied to the analysis of echocardiograms [37].…”

Simulation of Ground-Truth Validation Data Via Physically- and Statistically-Based Warps

“…In this work, we contribute to addressing the problem of scarcity of ground-truth data through the simulation of an arbitrarily large number of novel ground-truth datasets from a single reference data set and the creation of a web interface to this simulation tool. Although it is difficult to evaluate the validity and realism of the simulated data, we employ a physically-and statistically-based generative model to ensure data realism to a large degree by adopting the formulation proposed in [7]. We also extend [7] to operate on images rather than landmarks along contours of shapes, and extend it from 2D to 3D.…”

“…Although it is difficult to evaluate the validity and realism of the simulated data, we employ a physically-and statistically-based generative model to ensure data realism to a large degree by adopting the formulation proposed in [7]. We also extend [7] to operate on images rather than landmarks along contours of shapes, and extend it from 2D to 3D. While we focus on data simulation for validating or training generic, modalityindependent segmentation algorithms, the simulated images will possess appearance characteristics according to the modality of the reference data set.…”