18971447
Probabilistic Relaxation using the Heat Equation
In this paper a new formulation of probabilistic relaxation labeling is developed using the theory of diffusion processes on graphs. According to this picture, the label probabilities are given by the state-vector of a continuous time random walk on a support graph. The state-vector is the solution of the heat equation on the support-graph. The nodes of the support graph are the Cartesian product of the object-set and label-set of the relaxation process. The compatibility functions are combined in the weight matrix of the support graph. The solution of the heat-equation is found by exponentiating the eigensystem of the Laplacian matrix for the weighted support graph with time. We demonstrate the new relaxation process on a feature correspondence matching problem abstracted in terms of relational graphs
45076379
Kernel Spectral Correspondence Matching Using Label Consistency Constraints
This paper investigates a kernel spectral approach to the problem of point pattern matching. Our first contribution is to show how kernel principal components analysis can be effectively used for solving the point correspondence matching problem when the point-sets are subject to structural errors, i.e. they are of different size. Our second contribution is to show how label consistency constraints can be incorporated into the construction of the Gram matrices for solving the articulated point pattern matching problem. We compare our algorithm with earlier point matching approaches and provide experiments on both synthetic data and real world data.
31489027
A Graph Spectral Approach to Consistent Labelling
In this paper a new formulation of probabilistic relaxation labeling is developed using the theory of diffusion processes on graphs. Our idea is to formulate relaxation labelling as a diffusion process on the vector of object-label probabilities. According to this picture, the label probabilities are given by the state-vector of a continuous time random walk on a support graph. The state-vector is the solution of the heat equation on the support-graph. The nodes of the support graph are the Cartesian product of the object-set and label-set of the relaxation process. The compatibility functions are combined in the weight matrix of the support graph. The solution of the heat-equation is found by exponentiating the eigensystem of the Laplacian matrix for the weighted support graph with time. We demonstrate the new relaxation process on a toy labeling example which has been studied extensively in the early literature, and a feature correspondence matching problem abstracted in terms of relational graphs. The experiments show encouraging labeling and matching results.
19006969
Water drops on surfaces
We present a physically-based method to enforce contact angles at the intersection of fluid free surfaces and solid objects, allowing us to simulate a variety of small-scale fluid phenomena including water drops on surfaces. The heart of this technique is a virtual surface method, which modifies the level set distance field representing the fluid surface in order to maintain an appropriate contact angle. The surface tension that is calculated on the contact line between the solid surface and liquid surface can then capture all interfacial tensions, including liquid-solid, liquid-air and solid-air tensions. We use a simple dynamic contact angle model to select contact angles according to the solid material property, water history, and the fluid front's motion. Our algorithm robustly and accurately treats various drop shape deformations, and handles both flat and curved solid surfaces. Our results show that our algorithm is capable of realistically simulating several small-scale liquid phenomena such as beading and flattened drops, stretched and separating drops, suspended drops on curved surfaces, and capillary action.
7125775
User-Defined Aggregates in Database Languages
User-defined aggregates (UDAs) can be the linchpin of sophisticated data mining functions and other advanced database applications, but they find little support in current database systems. In this paper, we describe the SQL-AG prototype that overcomes these limitations by supporting UDAs as originally proposed in Postgres and SQL3. Then we extend the power and flexibility of UDAs by adding (i) early returns, (to express online aggregation) and (ii) syntactically recognizable monotonic UDAs that can be used in recursive queries to support applications, such as Bill of Materials (BoM) and greedy algorithms for graph optimization, that cannot be expressed under stratified aggregation. T his paper proposes a unified solution to both the theoretical and practical problems of UDAs, and demonstrates the power of UDAs in dealing with advanced database applications.
5516437
Compact reachability labeling for graph-structured data
Testing reachability between nodes in a graph is a well-known problem with many important applications, including knowledge representation, program analysis, and more recently, biological and ontology databases inferencing as well as XML query processing. Various approaches have been proposed to encode graph reachability information using node labeling schemes, but most existing schemes only work well for specific types of graphs. In this paper, we propose a novel approach, HLSS(Hierarchical Labeling of Sub-Structures), which identifies different types of substructures within a graph and encodes them using techniques suitable to the characteristics of each of them. We implement HLSS with an efficient two-phase algorithm, where the first phase identifies and encodes strongly connected components as well as tree substructures, and the second phase encodes the remaining reachability relationships by compressing dense rectangular submatrices in the transitive closure matrix. For the important subproblem of finding densest submatrices, we demonstrate the hardness of the problem and propose several practical algorithms. Experiments show that HLSS handles different types of graphs well, while existing approaches fall prey to graphs with substructures they are not designed to handle.
15278727
LOCI: Load Shedding through Class-Preserving Data Acquisition
An avalanche of data available in the stream form is overstretching our data analyzing ability. In this paper, we propose a novel load shedding method that enables fast and accurate stream data classification. We transform input data so that its class information concentrates on a few features, and we introduce a progressive classifier that makes prediction with partial input. We take advantage of stream data's temporal locality -for example, readings from a temperature sensor usually do not change dramatically over a short period of time -for load shedding. We first show that temporal locality of the original data is preserved by our transform, then we utilize positive and negative knowledge about the data (which is of much smaller size than the data itself) for classification. We employ both analytical and empirical analysis to demonstrate the advantage of our approach.
41114072
Real-Time 3D Motion Tracking with Known Geometric Models
In this paper a new model-based tracking algorithm is proposed for real-time performance. The matching process includes two aspects of: (1) feature extraction using local minimum energy and (2) global matching of known 3D models against the projected features. The algorithm is robust to change in lighting and background. The small motion hypothesis was used for fitting of feature energy which is defined as the negative absolute value of the edge strength. An autoregressiveAR(1) model is employed for detecting incorrect matches in terms of the feature energy. We have found a new invariance-based method to eliminate false matches caused by strong shadow or occlusion. The invariance is the ratio of trigonometric functions of the angles formed by a polygon. In order to calculate the vertices of the object surface in an image, regression technique in terms of matched features is efficient in our approach. A linear least squares method and the orthonormal rotation matrix are used for motion estimation and pose update of the six degrees of freedom. Also, an Extended Kalman Filter is introduced to guarantee a smooth motion estimation and prediction.