16121104
3D Surface Matching with Mutual Information and Riemann Surface Structures
Many medical imaging applications require the computation of dense correspondence vector fields that match one surface with another. Surface-based registration is useful for tracking brain change, registering functional imaging data from multiple subjects, and for creating statistical shape models of anatomy. To avoid the need for a large set of manually-defined landmarks to constrain these surface correspondences, we developed an algorithm to automate the matching of surface features. It extends the mutual information method to automatically match general 3D surfaces (including surfaces with a branching topology). We use diffeomorphic flows to optimally align the Riemann surface structures of two surfaces. First, we use holomorphic 1-forms to induce consistent conformal grids on both surfaces. High genus surfaces are mapped to a set of rectangles in the Euclidean plane, and closed genus-zero surfaces are mapped to the sphere. Next, we compute stable geometric features (mean curvature and the conformal factor) and pull them back as scalar fields onto the 2D parameter domains. Mutual information is used as a cost functional to drive a fluid flow in the parameter domain that optimally aligns these surface features. A diffeomorphic surface-tosurface mapping is then recovered that matches anatomy in 3D. Lastly, we present a spectral method that ensures that the grids induced on the target surface remain conformal when pulled through the correspondence field. Using the chain rule, we express the gradient of the mutual information between surfaces in the conformal basis of the source surface. This finite-dimensional linear space generates all conformal reparameterizations of the surface. Illustrative experiments show the method applied to hippocampal surface registration, a key step in subcortical shape analysis in Alzheimer’s disease and schizophrenia.
5267319
Volumetric harmonic brain mapping
We developed two different techniques to study volume mapping problem in Computer Graphics. The first one is to find a harmonic map from a 3 manifold to a 3D solid sphere and the second is a sphere carving algorithm which calculates the simplicial decomposition of volume adapted to surfaces. In this paper, we apply these two techniques to brain mapping problem. We use a tetrahedral mesh to represent the brain volume. The experimental results on both synthetic and brain volume data are reported. We suggest that 3D harmonic mapping of brain volumes to a solid sphere can provide a canonical coordinate system for feature identification and segmentation, as well as anatomical normalization.
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%.
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.
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.
16143751
Portrait video phone
As the Internet and wirless networks are developed rapidly, the demand of communicating anywhere, anytime on any device emerges. However, most of the current wireless networks still work in low bandwidths, and mobile devices still suffer from weak computational power, short battery lifetime and limited display capability. We developed portrait video phone systems that can run on Pcs and Pocket Pcs at very low bit rates through the Internet. The core technology that portrait video phones employ is the so-called portrait video (or bi-level video) codec. Portrait video codec first converts a full-color video into a black/white image sequence and then compresses it into a black/white portrait-like video. Portrait video processes clearer shape, smoother motion, shorter initial latency, and cheaper computational cost than MPEG2, MPEG4 and H.263 for low bandwidths. Typically the portrait video phone provides QCIF-size video with a frame rate of 5-15 fps for a 9.6 Kbps video bandwidth. The portrait video is so small that it can even be transmitted through an HTTP proxy as text. Experiments show that the portrait video phones work well on ordinary GSM wireless telecommunication networks.
2800311
Conformal Geometry and Its Applications on 3D Shape Matching, Recognition, and Stitching
Three-dimensional shape matching is a fundamental issue in computer vision with many applications such as shape registration, 3D object recognition, and classification. However, shape matching with noise, occlusion, and clutter is a challenging problem. In this paper, we analyze a family of quasi-conformal maps including harmonic maps, conformal maps, and least-squares conformal maps with regards to 3D shape matching. As a result, we propose a novel and computationally efficient shape matching framework by using least-squares conformal maps. According to conformal geometry theory, each 3D surface with disk topology can be mapped to a 2D domain through a global optimization and the resulting map is a diffeomorphism, i.e., one-to-one and onto. This allows us to simplify the 3D shape-matching problem to a 2D image-matching problem, by comparing the resulting 2D parametric maps, which are stable, insensitive to resolution changes and robust to occlusion, and noise. Therefore, highly accurate and efficient 3D shape matching algorithms can be achieved by using the above three parametric maps. Finally, the robustness of least-squares conformal maps is evaluated and analyzed comprehensively in 3D shape matching with occlusion, noise, and resolution variation. In order to further demonstrate the performance of our proposed method, we also conduct a series of experiments on two computer vision applications, i.e., 3D face recognition and 3D nonrigid surface alignment and stitching.
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.
125037919
Perceptual Scale Space and its Applications
In this paper, we study a perceptual scale space by constructing a so-called sketch pyramid which augments the Gaussian and Laplacian pyramid representations in traditional image scale space theory. Each level of this sketch pyramid is a generic attributed graph - called the primal sketch which is inferred from the corresponding image at the same level of the Gaussian pyramid. When images are viewed at increasing resolutions, more details are revealed. This corresponds to perceptual transitions which are represented by topological changes in the sketch graph in terms of a graph grammar. We compute the sketch or perceptual pyramid by Bayesian inference upwards-downwards the pyramid using Markov chain Monte Carlo reversible jumps. We show two example applications of this perceptual scale space: (1) motion tracking of objects over scales, and (2) adaptive image displays which can efficiently show a large high resolution image in a small screen (of a PDA for example) through a selective tour of its image pyramid. Other potential applications include super resolution and multiresolution object recognition.
18101194
The Real-Time Process Algebra (RTPA)
The real-time process algebra (RTPA) is a set of new mathematical notations for formally describing system architectures, and static and dynamic behaviors. It is recognized that the specification of software behaviors is a three-dimensional problem known as: (i) mathematical operations, (ii) event/process timing, and (iii) memory manipulations. Conventional formal methods in software engineering were designed to describe the 1-D (type (i)) or 2-D (types (i) and (iii)) static behaviors of software systems via logic, set and type theories. However, they are inadequate to address the 3-D problems in real-time systems. A new notation system that is capable to describe and specify the 3-D real-time behaviors, the real-time process algebra (RTPA), is developed in this paper to meet the fundamental requirements in software engineering.RTPA is designed as a coherent software engineering notation system and a formal engineering method for addressing the 3-D problems in software system specification, refinement, and implementation, particularly for real-time and embedded systems. In this paper, the RTPA meta-processes, algebraic relations, system architectural notations, and a set of fundamental primary and abstract data types are described. On the basis of the RTPA notations, a system specification method and a refinement scheme of RTPA are developed. Then, a case study on a telephone switching system is provided, which demonstrates the expressive power of RTPA on formal specification of both software system architectures and behaviors. RTPA elicits and models 32 algebraic notations, which are the common core of existing formal methods and modern programming languages. The extremely small set of formal notations has been proven sufficient for modeling and specifying real-time systems, their architecture, and static/dynamic behaviors in real-world software engineering environment.