1,593 research outputs found
An Image Morphing Technique Based on Optimal Mass Preserving Mapping
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On Visualizing Branched Surface: an Angle/Area Preserving Approach
The techniques of surface deformation and mapping are useful tools for the visualization of medical surfaces, especially for highly undulated or branched surfaces. In this thesis, two algorithms
are presented for flattened visualizations of multi-branched medical surfaces, such as vessels. The first algorithm is an angle preserving approach, which is based on conformal analysis. The mapping function is obtained by minimizing two Dirichlet functionals. On a triangulated representation of vessel surfaces, this algorithm can be implemented efficiently using a finite
element method. The second algorithm adjusts the result from conformal mapping to produce a flattened representation of the original surface while preserving areas. It employs the theory of
optimal mass transport via a gradient descent approach.
A new class of image morphing algorithms is also considered based on the theory of optimal mass transport. The mass moving energy functional is revised by adding an intensity penalizing term, in
order to reduce the undesired "fading" effects. It is a parameter free approach. This technique has been applied on several natural and medical images to generate in-between image sequences.Ph.D.Allen Tannenbaum Committee Chair
Anthony J. Yezzi, Committee Member;
James Gruden, Committee Member;
May D. Wang, Committee Member;
Oskar Skrinjar, Committee Membe
Representing an Object by Interchanging What with Where
Exploring representations is a fundamental step towards understanding vision. The visual system carries two types of information along separate pathways: One is about what it is and the other is about where it is. Initially, the what is represented by a pattern of activity that is distributed across millions of photoreceptors, whereas the where is 'implicitly' given as their retinotopic positions. Many computational theories of object recognition rely on such pixel-based representations, but they are insufficient to learn spatial information such as position and size due to the implicit encoding of the where information. 
Here we try transforming a retinal image of an object into its internal image via interchanging the what with the where, which means that patterns of intensity in internal image describe the spatial information rather than the object information. To be concrete, the retinal image of an object is deformed and turned over into a negative image, in which light areas appear dark and vice versa, and the object's spatial information is quantified with levels of intensity on borders of that image. 
Interestingly, the inner part excluding the borders of the internal image shows the position and scale invariance. In order to further understand how the internal image associates the what and where, we examined the internal image of a face which moves or is scaled on the retina. As a result, we found that the internal images form a linear vector space under the object translation and scaling. 
In conclusion, these results show that the what-where interchangeability might play an important role for organizing those two into internal representation of brain
A Survey of Morphing Techniques
Image morphing provides the tool to generate the flexible and powerful visual effect. Morphing depicts the transformation of one image into another image. The process of image morphing starts with the feature specification phase and then proceeds to warp generation phase, followed by the transition control phase. This paper surveys the various techniques available for all three stages of image morphing
Diffeomorphic density matching by optimal information transport
We address the following problem: given two smooth densities on a manifold,
find an optimal diffeomorphism that transforms one density into the other. Our
framework builds on connections between the Fisher-Rao information metric on
the space of probability densities and right-invariant metrics on the
infinite-dimensional manifold of diffeomorphisms. This optimal information
transport, and modifications thereof, allows us to construct numerical
algorithms for density matching. The algorithms are inherently more efficient
than those based on optimal mass transport or diffeomorphic registration. Our
methods have applications in medical image registration, texture mapping, image
morphing, non-uniform random sampling, and mesh adaptivity. Some of these
applications are illustrated in examples.Comment: 35 page
Structural Surface Mapping for Shape Analysis
Natural surfaces are usually associated with feature graphs, such as the cortical surface with anatomical atlas structure. Such a feature graph subdivides the whole surface into meaningful sub-regions. Existing brain mapping and registration methods did not integrate anatomical atlas structures. As a result, with existing brain mappings, it is difficult to visualize and compare the atlas structures. And also existing brain registration methods can not guarantee the best possible alignment of the cortical regions which can help computing more accurate shape similarity metrics for neurodegenerative disease analysis, e.g., Alzheimer’s disease (AD) classification. Also, not much attention has been paid to tackle surface parameterization and registration with graph constraints in a rigorous way which have many applications in graphics, e.g., surface and image morphing.
This dissertation explores structural mappings for shape analysis of surfaces using the feature graphs as constraints. (1) First, we propose structural brain mapping which maps the brain cortical surface onto a planar convex domain using Tutte embedding of a novel atlas graph and harmonic map with atlas graph constraints to facilitate visualization and comparison between the atlas structures. (2) Next, we propose a novel brain registration technique based on an intrinsic atlas-constrained harmonic map which provides the best possible alignment of the cortical regions. (3) After that, the proposed brain registration technique has been applied to compute shape similarity metrics for AD classification. (4) Finally, we propose techniques to compute intrinsic graph-constrained parameterization and registration for general genus-0 surfaces which have been used in surface and image morphing applications
Barycenters of Natural Images -- Constrained Wasserstein Barycenters for Image Morphing
Image interpolation, or image morphing, refers to a visual transition between
two (or more) input images. For such a transition to look visually appealing,
its desirable properties are (i) to be smooth; (ii) to apply the minimal
required change in the image; and (iii) to seem "real", avoiding unnatural
artifacts in each image in the transition. To obtain a smooth and
straightforward transition, one may adopt the well-known Wasserstein Barycenter
Problem (WBP). While this approach guarantees minimal changes under the
Wasserstein metric, the resulting images might seem unnatural. In this work, we
propose a novel approach for image morphing that possesses all three desired
properties. To this end, we define a constrained variant of the WBP that
enforces the intermediate images to satisfy an image prior. We describe an
algorithm that solves this problem and demonstrate it using the sparse prior
and generative adversarial networks
On Nonrigid Shape Similarity and Correspondence
An important operation in geometry processing is finding the correspondences
between pairs of shapes. The Gromov-Hausdorff distance, a measure of
dissimilarity between metric spaces, has been found to be highly useful for
nonrigid shape comparison. Here, we explore the applicability of related shape
similarity measures to the problem of shape correspondence, adopting spectral
type distances. We propose to evaluate the spectral kernel distance, the
spectral embedding distance and the novel spectral quasi-conformal distance,
comparing the manifolds from different viewpoints. By matching the shapes in
the spectral domain, important attributes of surface structure are being
aligned. For the purpose of testing our ideas, we introduce a fully automatic
framework for finding intrinsic correspondence between two shapes. The proposed
method achieves state-of-the-art results on the Princeton isometric shape
matching protocol applied, as usual, to the TOSCA and SCAPE benchmarks
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