Kernel Fisher discriminant for shape-based classification in epilepsy

Kodipaka, Santhosh; Vemuri, Baba C.; Rangarajan, Anand; Leonard, Christiana M.; Schmallfuss, I.; Eisenschenk, Stephan

doi:10.1016/j.media.2006.10.002

Cited by 24 publications

(26 citation statements)

References 16 publications

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“…9. Studies have shown that distinguishing between LATL and RATL in epilepsy is a hard problem and that we need sophisticated features in order to automatically classify them (Kodipaka et al (2007)). Tables 2 and 3 indicate that the indices for both LATL and RATL are similar hence the left and right anterior medial temporal lobe focuses are indistinguishable w.r.t.…”

Section: Shape Variation Analysismentioning

confidence: 99%

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Construction of a neuroanatomical shape complex atlas from 3D MRI brain structures

et al. 2012

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Brain atlas construction has attracted significant attention lately in the neuroimaging community due to its application to the characterization of neuroanatomical shape abnormalities associated with various neurodegenerative diseases or neuropsychiatric disorders. Existing shape atlas construction techniques usually focus on the analysis of a single anatomical structure in which the important inter-structural information is lost. This paper proposes a novel technique for constructing a neuroanatomical shape complex atlas based on an information geometry framework. A shape complex is a collection of neighboring shapes-for example, the thalamus, amygdala and the hippocampus circuit-which may exhibit changes in shape across multiple structures during the progression of a disease. In this paper, we represent the boundaries of the entire shape complex using the zero level set of a distance transform function S(x). We then re-derive the relationship between the stationary state wave function ψ(x) of the Schrödinger equation − 2 ∇ 2 ψ + ψ = 0 and the eikonal equation ∇S = 1 satisfied by any distance function. This leads to a one-to-one map (up to scale) between ψ(x) and S(x) via an explicit relationship. We further exploit this relationship by mapping ψ(x) to a unit hypersphere whose Riemannian structure is fully known, thus effectively turn ψ(x) into the square-root of a probability density * Corresponding author * * Principal corresponding author Email addresses: tichen@cise.ufl.edu (Ting Chen), anand@cise.ufl.edu (Anand Rangarajan), stephan.eisenschenk@neurology.ufl.edu (Stephan J. Eisenschenk), vemuri@cise.ufl.edu (Baba C. Vemuri) Preprint submitted to NeuroImageOctober 11, 2012 function. This allows us to make comparisons-using elegant, closed-form analytic expressions-between shape complexes represented as square-root densities. A shape complex atlas is constructed by computing the Karcher meanψ(x) in the space of square-root densities and then inversely mapping it back to the space of distance transforms in order to realize the atlas shape. We demonstrate the shape complex atlas computation technique via a set of experiments on a population of brain MRI scans including controls and epilepsy patients with either right anterior medial temporal or left anterior medial temporal lobectomies.

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Section: Shape Variation Analysismentioning

confidence: 99%

“…volume based analysis. A promising immediate avenue for future research (following Kodipaka et al (2007)) is to utilize the histogram of the deformation field between the shape complex of the subject and the atlas for further analysis. In our approach, a single distance transform is used to represent a shape complex.…”

Section: Shape Variation Analysismentioning

confidence: 99%

Construction of a neuroanatomical shape complex atlas from 3D MRI brain structures

et al. 2012

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“…the intersection of two hyperplanes. With these constraints, the boundary (Eqn.2) in ℋ can also be written as: (7) Since ℋ ≡ ℝ M − 2 , let us track the section of the discriminant boundary, ∩ ℋ. Let X ∈ ℋ and the distance between a focus point F k and its orthogonal projection in ℋ, be .…”

Section: Finding Nearest Point For Fixed {H 1 (X) H 2 (X)}mentioning

confidence: 99%

“…We encounter such high dimensional sparse datasets in several computer vision and learning applications, such as in the diagnosis of Epilepsy based on brain MRI scans [7], the diagnosis of various types of Cancer from micro-array gene expression data [1], and speech recognition. Stated formally, the supervised learning problem is severely under constrained when one is given N labeled data points that lie in ℝ M where N ≪ M.…”

Section: Introductionmentioning

confidence: 99%

Large margin pursuit for a Conic Section classifier

Kodipaka

Banerjee

Vemuri

2008

2008 IEEE Conference on Computer Vision and Pattern Recognition

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Learning a discriminant becomes substantially more difficult when the datasets are high-dimensional and the available samples are few. This is often the case in computer vision and medical diagnosis applications. A novel Conic Section classifier (CSC) was recently introduced in the literature to handle such datasets, wherein each class was represented by a conic section parameterized by its focus, directrix and eccentricity. The discriminant boundary was the locus of all points that are equieccentric relative to each class-representative conic section. Simpler boundaries were preferred for the sake of generalizability.In this paper, we improve the performance of the two-class classifier via a large margin pursuit. When formulated as a non-linear optimization problem, the margin computation is demonstrated to be hard, especially due to the high dimensionality of the data. Instead, we present a geometric algorithm to compute the distance of a point to the nonlinear discriminant boundary generated by the CSC in the input space. We then introduce a large margin pursuit in the learning phase so as to enhance the generalization capacity of the classifier. We validate the algorithm on real datasets and show favorable classification rates in comparison to many existing state-of-the-art binary classifiers as well as the CSC without margin pursuit.

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“…Another recent approach proposes an entropy based criterion to find shape correspondences, but requires implicit surface representations [9]. Other recent methods combine the shape analysis with the search for correspondences, however, these methods are not easily adaptable to multiple observations of unstructured point sets [10,11,12] or focus only on the mean shape [13]. In order to build an SSM based on inexact correspondences between point clouds, we pursue a probabilistic concept and base our work on a EM-ICP registration algorithm which proved to be robust, precise, and fast [14].…”

Section: Introductionmentioning

confidence: 99%

Shape Analysis Using a Point-Based Statistical Shape Model Built on Correspondence Probabilities

Hufnagel

Pennec

Ehrhardt

et al.

Medical Image Computing and Computer-Assisted Intervention – MICCAI 2007

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Abstract.A fundamental problem when computing statistical shape models is the determination of correspondences between the instances of the associated data set. Often, homologies between points that represent the surfaces are assumed which might lead to imprecise mean shape and variability results. We propose an approach where exact correspondences are replaced by evolving correspondence probabilities. These are the basis for a novel algorithm that computes a generative statistical shape model. We developed an unified MAP framework to compute the model parameters ('mean shape' and 'modes of variation') and the nuisance parameters which leads to an optimal adaption of the model to the set of observations. The registration of the model on the instances is solved using the Expectation Maximization -Iterative Closest Point algorithm which is based on probabilistic correspondences and proved to be robust and fast. The alternated optimization of the MAP explanation with respect to the observation and the generative model parameters leads to very efficient and closed-form solutions for (almost) all parameters. Experimental results on brain structure data sets demonstrate the efficiency and well-posedness of the approach. The algorithm is then extended to an automatic classification method using the k-means clustering and applied to synthetic data as well as brain structure classification problems.

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Kernel Fisher discriminant for shape-based classification in epilepsy

Cited by 24 publications

References 16 publications

Construction of a neuroanatomical shape complex atlas from 3D MRI brain structures

Construction of a neuroanatomical shape complex atlas from 3D MRI brain structures

Large margin pursuit for a Conic Section classifier

Shape Analysis Using a Point-Based Statistical Shape Model Built on Correspondence Probabilities

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