Shape-based 3D surface correspondence using geodesics and local geometry

Wang, Y.; Peterson, Bradley S.; Staib, Lawrence H.

doi:10.1109/cvpr.2000.854933

Cited by 91 publications

(67 citation statements)

References 16 publications

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“…Most previous approaches to automated and semiautomated landmark generation and registration of 3D-surfaces use the local surface geometry. Examples of this are the non-rigid registration technique by Feldmar and Ayache [3], the local geometry and surface geodesic approach by Wang et al [4] and the surface signature technique by Yamany et al [5]. A method for automatic landmark generation based on a symmetric version of the iterative closest point algorithm is presented in [6].…”

Section: Introductionmentioning

confidence: 99%

Building and Testing a Statistical Shape Model of the Human Ear Canal

Paulsen

Larsen

Nielsen

et al. 2002

Lecture Notes in Computer Science

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Abstract. Today the design of custom in-the-ear hearing aids is based on personal experience and skills and not on a systematic description of the variation of the shape of the ear canal. In this paper it is described how a dense surface point distribution model of the human ear canal is built based on a training set of laser scanned ear impressions and a sparse set of anatomical landmarks placed by an expert. The landmarks are used to warp a template mesh onto all shapes in the training set. Using the vertices from the warped meshes, a 3D point distribution model is made. The model is used for testing for gender related differences in size and shape of the ear canal.

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Section: Introductionmentioning

confidence: 99%

Building and Testing a Statistical Shape Model of the Human Ear Canal

Paulsen

Larsen

Nielsen

et al. 2002

Lecture Notes in Computer Science

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“…Due to the convoluted nature and variability among different brains, mapping of the cortical surfaces poses many numerical challenges for classical surface matching algorithms such as the iterative closest point(ICP) method (Besl and McKay, 1992) and its extension in brain mapping (Wang et al, 2000). Thus, the cortical mapping problem is conventionally solved through an indirect approach as illustrated in Fig.…”

Section: Introductionmentioning

confidence: 99%

Direct cortical mapping via solving partial differential equations on implicit surfaces

Shi

Thompson

Dinov

et al. 2007

Medical Image Analysis

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In this paper, we propose a novel approach for cortical mapping that computes a direct map between two cortical surfaces while satisfying constraints on sulcal landmark curves. By computing the map directly, we can avoid conventional intermediate parameterizations and help simplify the cortical mapping process. The direct map in our method is formulated as the minimizer of a flexible variational energy under landmark constraints. The energy can include both a harmonic term to ensure smoothness of the map and general data terms for the matching of geometric features. Starting from a properly designed initial map, we compute the map iteratively by solving a partial differential equation (PDE) defined on the source cortical surface. For numerical implementation, a set of adaptive numerical schemes are developed to extend the technique of solving PDEs on implicit surfaces such that landmark constraints are enforced. In our experiments, we show the flexibility of the direct mapping approach by computing smooth maps following landmark constraints from two different energies. We also quantitatively compare the metric preserving property of the direct mapping method with a parametric mapping method on a group of 30 subjects. Finally, we demonstrate the direct mapping method in the brain mapping applications of atlas construction and variability analysis.

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“…The problem of these mappings is that they only work well for sphere-like shapes, which is not the case for the CC. Other investigators used conformal mapping to flatten colon surface [252], surface matching using geodesic and local geometry to locate correspondences between two surface points [253], harmonic shape images to map a 3D surface patch with disc topology to a 2D domain and encode the shape information of the surface patch into the 2D image [254], harmonics differentials to unfold colon wall volume [255], and solving the Poisson equation to extract useful shape features of a closed 2D object [256].…”

Section: Trendsmentioning

confidence: 99%

Developing advanced mathematical models for detecting abnormalities in 2D/3D medical structures.

Elnakib¹

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DEDICATIONThis dissertation is dedicated to my mother, my father, and my wife for their love, patience, and support during the completion of this endeavor.iii ACKNOWLEDGMENTSIn the Name of Allah, the most beneficent, the most merciful. All deepest thanks are due to Allah, the compassionate for the uncountable gifts given to me.I would like to express my sincere gratitude to Professor El-Baz, my dissertation advisor, for the immeasurable amount of support and guidance he has provided throughout this study. He gave me the opportunity to work in his distinguished research group and provided me with an exciting working environment that facilitate many opportunities to develop new ideas and working on promising applications. Dr. El-Baz is always willing to give, share, and appreciate. I knew that I could always expect full credit for my accomplishments. He always supported me with novel ideas that helped me to publish my works in the top international conference and journal papers. It is worthy to mention that Professor El-Baz is a great advisor as well as a good friend who helps any Ph.D. student who works with him in high energy level. I cannot thank him enough, and shall remain grateful for all he has done. Detecting abnormalities in two-dimensional (2D) and three-dimensional (3D) medical structures is among the most interesting and challenging research areas in the medical imaging field. Obtaining the desired accurate automated quantification of abnormalities in medical structures is still very challenging. This is due to a large and constantly growing number of different objects of interest and associated abnormalities, large variations of their appearances and shapes in images, different medical imaging modalities, and associated changes of signal homogeneity and noise for each object. The main objective of this dissertation is to address these problems and to provide proper mathematical models and techniques that are capable of analyzing low and high resolution medical data and providing an accurate, automated analysis of the abnormalities in medical structures in terms of their area/volume, shape, and associated abnormal functionality.This dissertation presents different preliminary mathematical models and techniques that are applied in three case studies: (i) detecting abnormal tissue in vi the left ventricle (LV) wall of the heart from delayed contrast-enhanced cardiac magnetic resonance images (MRI), (ii) detecting local cardiac diseases based on estimating the functional strain metric from cardiac cine MRI, and (iii) identifying the abnormalities in the corpus callosum (CC) brain structure-the largest fiber bundle that connects the two hemispheres in the brain-for subjects that suffer from developmental brain disorders. For detecting the abnormal tissue in the heart, a graph-cut mathematical optimization model with a cost function that accounts for the object's visual appearance and shape is used to segment the the inner cavity. The model is further integrated with a geometric model (i.e., a fast marching...

show abstract

Shape-based 3D surface correspondence using geodesics and local geometry

Cited by 91 publications

References 16 publications

Building and Testing a Statistical Shape Model of the Human Ear Canal

Building and Testing a Statistical Shape Model of the Human Ear Canal

Direct cortical mapping via solving partial differential equations on implicit surfaces

Developing advanced mathematical models for detecting abnormalities in 2D/3D medical structures.

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