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In this paper, we introduce a novel framework for computing a path of diffeomorphisms between a pair of input diffeomorphisms. Direct computation of a geodesic path on the space of diffeomorphisms Diff(Ω) is difficult, and it can be attributed mainly to the infinite dimensionality of Diff(Ω). Our proposed framework, to some degree, bypasses(More)
This paper presents an application of a recently introduced novel framework for computing the diffeomorphic path between two given diffeomorphisms computed from two pairs of image frames in a motion sequence [1]. The specific application we address here is that of cardiac motion analysis. The framework involves a two-step algorithm wherein we first project(More)
Manifold-valued datasets are widely encountered in many computer vision tasks. A non-linear analog of the PCA algorithm, called the Principal Geodesic Analysis (PGA) algorithm suited for data lying on Riemannian manifolds was reported in literature a decade ago. Since the objective function in the PGA algorithm is highly non-linear and hard to solve(More)
Complex diffusion was introduced in image processing literature as a means to achieve simultaneous denoising and enhancement of scalar valued images. In this paper, we present a novel geometric framework for achieving complex diffusion on color images expressed as image graphs. In this framework, we develop a new variational formulation for achieving(More)
2011 c ⃝ 2011 Ting Chen 2 To Eva and thank her for acting as a very well behaved newborn baby To my husband Ying and my parents 3 ACKNOWLEDGMENTS I would like to first thank my advisors Dr. Baba C. Vemuri and Dr. Anand Rangarajan, without whom the thesis wouldn't have existed. Their strong passion, profound knowledge and endless innovative ideas for(More)
Deformable (2D or 3D) medical image registration is a challenging problem. Existing approaches assume that the underlying deformation is smooth. This smoothness assumption allows for solving the deformable registration at a coarse resolution and interpolate for finer resolutions. However, sliding of organs and breathing motion, exhibit discontinuities. We(More)
2012 c ⃝ 2012 Guang Cheng 2 To my wife Yandi, my daughter Lerong, and my parents 3 ACKNOWLEDGMENTS I would like to gratefully thank Dr. Baba Vemuri my major advisor, for his insightful guidance, unflinching patience and encouragement throughout my PhD study. This dissertation would not have been written without his guidance and support. I would also like to(More)
Images are often considered as functions defined on the image domains, and as functions, their (intensity) values are usually considered to be invariant under the image domain transforms. This functional viewpoint is both influential and prevalent, and it provides the justification for comparing images using functional $$\mathbf {L}^p$$ L p -norms. However,(More)
This paper proposes a geometric approach for comparing tensor-valued images (tensor fields) that is based on the idea of matching intrinsically low-dimensional shapes embedded in a higher-dimensional ambient space. More specifically, instead of regarding the tensor fields as tensor-valued functions defined on a given (image) domain, we consider their image(More)
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