Histogram Statistics of Local Model-Relative Image Regions

Abstract

Abstract. We present a novel approach to statistically characterize histograms of model-relative image regions. A multiscale model is used as an aperture to define image regions at multiple scales. We use this image description to define an appearance model for deformable model segmentation. Appearance models measure the likelihood of an object given a target image. To determine this likelihood we compute pixel intensity histograms of local model-relative image regions from a 3D image volume near the object boundary. We use a Gaussian model to statistically characterize the variation of non-parametric histograms mapped to Euclidean space using the Earth Mover's distance.The new method is illustrated and evaluated in a deformable model segmentation study on CT images of the human bladder, prostate, and rectum. Results show improvement over a previous profile based appearance model, out-performance of statistically modeled histograms over simple histogram measurements, and advantages of regional histograms at a fixed local scale over a fixed global scale.

Automatic Segmentation of the Bladder Using Deformable Models

“…Shape deformation approaches include geometric [9,10] and parametric [11] deformable models. They are quite flexible, since shape priors may be incorporated [9,12,2,13,3,10], an atlas can serve as initialization [14], they can be made to follow fuzzy criteria [11], and they allow for more than one structure to evolve simultaneously (e.g.…”

“…They are quite flexible, since shape priors may be incorporated [9,12,2,13,3,10], an atlas can serve as initialization [14], they can be made to follow fuzzy criteria [11], and they allow for more than one structure to evolve simultaneously (e.g. the prostate and bladder, as in [2]).…”

Deep Structure of Images in Populations Via Geometric Models in Populations

“…The first point is buttressed by results of Sean Ho's dissertation [2004] that probability distributions on intensities in an along-object-boundary scale space are more generalizable and specific than the more commonly used ones that are local in alongboundary location. The second point, regarding the benefits of the uses of probabilities on regional histograms, is discussed in the companion paper by Broadhurst et al [2005].…”

“…In the companion paper by Broadhurst et al [2005], a histogram representation in terms of average quantile values of the histogram is described that has the desired property: moving along geodesics according to an Earth Mover's distance. Thus, principal component analysis in this space is a useful way of forming probability distributions on histograms.…”

“…In effect, this means that the bin sizes of the histograms should increase with spatial scale and that the bins should overlap, having soft edges. This might be done directly, but it is probably preferable to do it on the Earth Mover's features of histograms produced by Gaussian-weighted average quantile values of histograms [Broadhurst 2005]. …”