13869510
Optimal global conformal surface parameterization
All orientable metric surfaces are Riemann surfaces and admit global conformal parameterizations. Riemann surface structure is a fundamental structure and governs many natural physical phenomena, such as heat diffusion and electro-magnetic fields on the surface. A good parameterization is crucial for simulation and visualization. This paper provides an explicit method for finding optimal global conformal parameterizations of arbitrary surfaces. It relies on certain holomorphic differential forms and conformal mappings from differential geometry and Riemann surface theories. Algorithms are developed to modify topology, locate zero points, and determine cohomology types of differential forms. The implementation is based on a finite dimensional optimization method. The optimal parameterization is intrinsic to the geometry, preserves angular structure, and can play an important role in various applications including texture mapping, remeshing, morphing and simulation. The method is demonstrated by visualizing the Riemann surface structure of real surfaces represented as triangle meshes.
3331857
Table Detection via Probability Optimization
In this paper, we define the table detection problem as a probability optimization problem. We begin, as we do in our previous algorithm, finding and validating each detected table candidates. We proceed to compute a set of probability measurements for each of the table entities. The computation of the probability measurements takes into consideration tables, table text separators and table neighboring text blocks. Then, an iterative updating method is used to optimize the page segmentation probability to obtain the final result. This new algorithm shows a great improvement over our previous algorithm. The training and testing data set for the algorithm include 1, 125 document pages having 518 table entities and a total of 10, 934 cell entities. Compared with our previous work, it raised the accuracy rate to 95.67% from 90.32% and to 97.05% from 92.04%.
2521415
Brain Surface Conformal Parameterization
We develop a general approach that uses holomorphic 1forms to parameterize anatomical surfaces with complex (possibly branching) topology. Rather than evolve the surface geometry to a plane or sphere, we instead use the fact that all orientable surfaces are Riemann surfaces and admit conformal structures, which induce special curvilinear coordinate systems on the surfaces. We can then automatically partition the surface using a critical graph that connects zero points in the conformal structure on the surface. The trajectories of iso-parametric curves canonically partition a surface into patches. Each of these patches is either a topological disk or a cylinder and can be conformally mapped to a parallelogram by integrating a holomorphic 1-form defined on the surface. The resulting surface subdivision and the parameterizations of the components are intrinsic and stable. To illustrate the technique, we computed conformal structures for several types of anatomical surfaces in MRI scans of the brain, including the cortex, hippocampus, and lateral ventricles. We found that the resulting parameterizations were consistent across subjects, even for branching structures such as the ventricles, which are otherwise difficult to parameterize. Compared with other variational approaches based on surface inflation, our technique works on surfaces with arbitrary complexity while guaranteeing minimal distortion in the parameterization. It also generates grids on surfaces for PDE-based signal processing.
5121588
Brain Surface Parameterization Using Riemann Surface Structure
We develop a general approach that uses holomorphic 1-forms to parameterize anatomical surfaces with complex (possibly branching) topology. Rather than evolve the surface geometry to a plane or sphere, we instead use the fact that all orientable surfaces are Riemann surfaces and admit conformal structures, which induce special curvilinear coordinate systems on the surfaces. Based on Riemann surface structure, we can then canonically partition the surface into patches. Each of these patches can be conformally mapped to a parallelogram. The resulting surface subdivision and the parameterizations of the components are intrinsic and stable. To illustrate the technique, we computed conformal structures for several types of anatomical surfaces in MRI scans of the brain, including the cortex, hippocampus, and lateral ventricles. We found that the resulting parameterizations were consistent across subjects, even for branching structures such as the ventricles, which are otherwise difficult to parameterize. Compared with other variational approaches based on surface inflation, our technique works on surfaces with arbitrary complexity while guaranteeing minimal distortion in the parameterization. It also offers a way to explicitly match landmark curves in anatomical surfaces such as the cortex, providing a surface-based framework to compare anatomy statistically and to generate grids on surfaces for PDE-based signal processing.
3357707
A method for document zone content classification
This paper describes an algorithm to classify each given document zone into one of nine classes and provides a protocol for its performance evaluation. The classification scheme uses an optimized binary decision tree and Viterbi algorithm for HMM to find the optimal solution. Our algorithm was trained and tested on a total of 24,177 zones within the 1600 images from UWCDROM III database. Its accuracy rate is 98.45% with a mean false alarm rate of 0.50%.
5987381
Algorithm performance contest
This contest involved the running and evaluation of computer vision and pattern recognition techniques on different data sets with known groundwidth. The contest included three areas; binary shape recognition, symbol recognition and image flow estimation. A package was made available for each area. Each package contained either real images with manual groundtruth or programs to generate data sets of ideal as well as noisy images with known groundtruth. They also contained programs to evaluate the results of an algorithm according to the given groundtruth. These evaluation criteria included the generation of confusion matrices, computation of the misdetection and false alarm rates and other performance measures suitable for the problems. The paper summarizes the data generation for each area and experimental results for a total of six participating algorithms.
15443235
Computing the Writhing Number of a Polygonal Knot
AbstractThe writhing number measures the global geometry of
 a closed space curve or knot.
 We show that this measure is related to the average winding number
 of its Gauss map.
 Using this relationship, we give an algorithm for computing
 the writhing number for a polygonal knot with n edges
 in time roughly proportional to n1.6.
 We also implement a different, simple algorithm and provide
 experimental evidence for its practical efficiency.


28306753
Low hardware complexity parallel turbo decoder architecture
Turbo decoders inherently have low throughput and long latency because of iterative decoding. Parallel processing is a powerful technique for high-throughput applications but often comes with large hardware complexity penalties. In this paper, we present a generic low hardware complexity parallel turbo decoder architecture, which enables multiple soft-input soft-output (SISO) decoders to process one data frame simultaneously. It can achieve multiple times the throughput of a typical serial decoder with a small fraction of hardware overhead. The proposed architecture works for any type of random interleavers, which makes it extremely useful in practical applications where turbo interleave patterns are not free to design. Based on estimation, the illustrated low hardware complexity 2-level parallel turbo decoding architecture can achieve twice the throughput of a typical serial decoding architecture with less than 20% hardware overhead when applied to 3rd generation CDMA systems.
14805900
Shape-based 3D surface correspondence using geodesics and local geometry
This paper describes a new method for determining correspondence between points on pairs of surfaces based on shape using a combination of geodesic distance and surface curvature. An initial sparse set of corresponding points is generated using a shape-based matching procedure. Geodesic interpolation is employed in order to capture the complex surface. In addition, surface correspondence and triangulation are computed simultaneously in a hierarchical way. Results applied to human cerebral cortical surfaces are shown to evaluate the approach.
793367
3D Brain surface matching based on geodesics and local geometry
The non-rigid registration of surfaces is a complex and difficult task for which there are many important applications, such as comparing shape between deformable objects and comparing associated function. This paper presents a new approach for brain surface matching by determining the correspondence of 3D point sets between pairs of surfaces. The algorithm is based on shape using a combination of geodesic distance and surface curvature. There are two major procedures involved. An initial sparse set of corresponding points is first generated by matching local geometrical features. Geodesic distance interpolation is then employed hierarchically in order to capture the complex surface. By this scheme, surface correspondence and triangulation are computed simultaneously. Experiments applied to human cerebral cortical surfaces are shown to evaluate the approach. It is shown that the proposed method performs well for both surface matching and surface shape recovery.
8818017
Using Model Trees for Classification
Model trees, which are a type of decision tree with linear regression functions at the leaves, form the basis of a recent successful technique for predicting continuous numeric values. They can be applied to classification problems by employing a standard method of transforming a classification problem into a problem of function approximation. Surprisingly, using this simple transformation the model tree inducer M5′, based on Quinlan's M5, generates more accurate classifiers than the state-of-the-art decision tree learner C5.0, particularly when most of the attributes are numeric.