1,314 research outputs found
An Image Morphing Technique Based on Optimal Mass Preserving Mapping
©2007 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or distribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE. This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder.DOI: 10.1109/TIP.2007.896637Image morphing, or image interpolation in the time domain, deals with the metamorphosis of one image into another. In this paper, a new class of image morphing algorithms is proposed based on the theory of optimal mass transport. The 2 mass moving energy functional is modified by adding an intensity penalizing term, in order to reduce the undesired double exposure effect. It is an intensity-based approach and, thus, is parameter free. The optimal warping function is computed using an iterative gradient descent approach. This proposed morphing method is also extended to doubly connected domains using a harmonic parameterization technique, along with finite-element methods
Density-equalizing maps for simply-connected open surfaces
In this paper, we are concerned with the problem of creating flattening maps
of simply-connected open surfaces in . Using a natural principle
of density diffusion in physics, we propose an effective algorithm for
computing density-equalizing flattening maps with any prescribed density
distribution. By varying the initial density distribution, a large variety of
mappings with different properties can be achieved. For instance,
area-preserving parameterizations of simply-connected open surfaces can be
easily computed. Experimental results are presented to demonstrate the
effectiveness of our proposed method. Applications to data visualization and
surface remeshing are explored
Preconditioned Nonlinear Conjugate Gradient Method of Stretch Energy Minimization for Area-Preserving Parameterizations
Stretch energy minimization (SEM) is widely recognized as one of the most
effective approaches for the computation of area-preserving mappings. In this
paper, we propose a novel preconditioned nonlinear conjugate gradient method
for SEM with guaranteed theoretical convergence. Numerical experiments indicate
that our new approach has significantly improved area-preserving accuracy and
computational efficiency compared to another state-of-the-art algorithm.
Furthermore, we present an application of surface registration to illustrate
the practical utility of area-preserving mappings as parameterizations of
surfaces.Comment: 18 pages, 8 figure
Bijective Density-Equalizing Quasiconformal Map for Multiply-Connected Open Surfaces
This paper proposes a novel method for computing bijective density-equalizing
quasiconformal (DEQ) flattening maps for multiply-connected open surfaces. In
conventional density-equalizing maps, shape deformations are solely driven by
prescribed constraints on the density distribution, defined as the population
per unit area, while the bijectivity and local geometric distortions of the
mappings are uncontrolled. Also, prior methods have primarily focused on
simply-connected open surfaces but not surfaces with more complicated
topologies. Our proposed method overcomes these issues by formulating the
density diffusion process as a quasiconformal flow, which allows us to
effectively control the local geometric distortion and guarantee the
bijectivity of the mapping by solving an energy minimization problem involving
the Beltrami coefficient of the mapping. To achieve an optimal parameterization
of multiply-connected surfaces, we develop an iterative scheme that optimizes
both the shape of the target planar circular domain and the density-equalizing
quasiconformal map onto it. In addition, landmark constraints can be
incorporated into our proposed method for consistent feature alignment. The
method can also be naturally applied to simply-connected open surfaces. By
changing the prescribed population, a large variety of surface flattening maps
with different desired properties can be achieved. The method is tested on both
synthetic and real examples, demonstrating its efficacy in various applications
in computer graphics and medical imaging
Surface Comparison with Mass Transportation
We use mass-transportation as a tool to compare surfaces (2-manifolds). In
particular, we determine the "similarity" of two given surfaces by solving a
mass-transportation problem between their conformal densities. This mass
transportation problem differs from the standard case in that we require the
solution to be invariant under global M\"obius transformations. Our approach
provides a constructive way of defining a metric in the abstract space of
simply-connected smooth surfaces with boundary (i.e. surfaces of disk-type);
this metric can also be used to define meaningful intrinsic distances between
pairs of "patches" in the two surfaces, which allows automatic alignment of the
surfaces. We provide numerical experiments on "real-life" surfaces to
demonstrate possible applications in natural sciences
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