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shantanu joshi

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Papers by shantanu joshi

Robust Stratified Sampling Plans for Low Selectivity Queries

International Conference on Data Engineering, 2008

We consider the problem of estimating the result of an aggregate query with a very low selectivit... more We consider the problem of estimating the result of an aggregate query with a very low selectivity. Traditional sampling techniques can be ineffective for such a problem since a small random sample is likely to miss most or even all of the records satisfying the restrictive selection predicate. Stratfied sampling is useful in this situation, but a key problem in applying stratified sampling effectively is identifying which strata are important and developing a sampling plan that favors those strata in a robust fashion. We develop a solution to this problem that combines any prior knowledge or expectation about the stratification with information obtained from pilot sampling in a principled Bayesian framework.

Online Estimation For Subset-Based SQL Queries

Very Large Data Bases, 2005

The largest databases in use today are so large that answering a query exactly can take minutes, ... more The largest databases in use today are so large that answering a query exactly can take minutes, hours, or even days. One way to address this problem is to make use of approximation algorithms. Previous work on online aggregation has considered how to give online estimates with everincreasing accuracy for aggregate functions over relational join and selection queries. However, no existing work is applicable to online estimation over subset-based SQL queries-those queries with a correlated subquery linked to an outer query via a NOT EXISTS, NOT IN, EXISTS, or IN clause (other queries such as EXCEPT and INTERSECT can also be seen as subset-based queries). In this paper we develop algorithms for online estimation over such queries, and consider the difficult problem of providing probabilistic accuracy guarantees at all times during query execution.

A disk-based join with probabilistic guarantees

Proceedings of the 2005 ACM SIGMOD international conference on Management of data - SIGMOD '05, 2005

One of the most common operations in analytic query processing is the application of an aggregate... more One of the most common operations in analytic query processing is the application of an aggregate function to the result of a relational join. We describe an algorithm for computing the answer to such a query over large, disk-based input tables. The key innovation of our algorithm is that at all times, it provides an online, statistical estimator for the eventual answer to the query, as well as probabilistic confidence bounds. Thus, a user can monitor the progress of the join throughout its execution and stop the join when satisfied with the estimate's accuracy, or run the algorithm to completion with a total time requirement that is not much longer than other common join algorithms. This contrasts with other online join algorithms, which either do not offer such statistical guarantees or can only offer guarantees so long as the input data can fit into core memory.

Robust Stratified Sampling Plans for Low Selectivity Queries

2008 IEEE 24th International Conference on Data Engineering, 2008

We consider the problem of estimating the result of an aggregate query with a very low selectivit... more We consider the problem of estimating the result of an aggregate query with a very low selectivity. Traditional sampling techniques can be ineffective for such a problem since a small random sample is likely to miss most or even all of the records satisfying the restrictive selection predicate. Stratfied sampling is useful in this situation, but a key problem in applying stratified sampling effectively is identifying which strata are important and developing a sampling plan that favors those strata in a robust fashion. We develop a solution to this problem that combines any prior knowledge or expectation about the stratification with information obtained from pilot sampling in a principled Bayesian framework.

The Sort-Merge-Shrink join

ACM Transactions on Database Systems, 2006

One of the most common operations in analytic query processing is the application of an aggregate... more One of the most common operations in analytic query processing is the application of an aggregate function to the result of a relational join. We describe an algorithm called the Sort-Merge-Shrink (SMS) Join for computing the answer to such a query over large, disk-based input tables. The key innovation of the SMS join is that if the input data are clustered in a statistically random fashion on disk, then at all times, the join provides an online, statistical estimator for the eventual answer to the query as well as probabilistic confidence bounds. Thus, a user can monitor the progress of the join throughout its execution and stop the join when satisfied with the estimate's accuracy or run the algorithm to completion with a total time requirement that is not much longer than that of other common join algorithms. This contrasts with other online join algorithms, which either do not offer such statistical guarantees or can only offer guarantees so long as the input data can fit into main memory.

A disk-based join with probabilistic guarantees

International Conference on Management of Data, 2005

One of the most common operations in analytic query processing is the application of an aggregate... more One of the most common operations in analytic query processing is the application of an aggregate function to the result of a relational join. We describe an algorithm for computing the answer to such a query over large, disk-based input tables. The key innovation of our algorithm is that at all times, it provides an online, statistical estimator for the eventual answer to the query, as well as probabilistic confidence bounds. Thus, a user can monitor the progress of the join throughout its execution and stop the join when satisfied with the estimate's accuracy, or run the algorithm to completion with a total time requirement that is not much longer than other common join algorithms. This contrasts with other online join algorithms, which either do not offer such statistical guarantees or can only offer guarantees so long as the input data can fit into core memory.

Oracle real application testing

International Conference on Management of Data, 2008

This paper presents the Oracle solution for database testing delivered in the Oracle 11g Database... more

Materialized sample views for database approximation

Knowledge and Data Engineering, IEEE …, 2008

We consider the problem of creating a sample view of a database table. A sample view is an indexe... more We consider the problem of creating a sample view of a database table. A sample view is an indexed, materialized view that permits efficient sampling from an arbitrary range query over the view. Such "sample views" are very useful to applications that require random samples from a database: approximate query processing, online aggregation, data mining, and randomized algorithms are a few examples. Our core technical contribution is a new file organization called the ACE Tree that is suitable for organizing and indexing a sample view. One of the most important aspects of the ACE Tree is that it supports online random sampling from the view. That is, at all times, the set of records returned by the ACE Tree constitutes a statistically random sample of the database records satisfying the relational selection predicate over the view. Our paper presents experimental results that demonstrate the utility of the ACE Tree.

The Sort-Merge-Shrink join

ACM Transactions on Database Systems, 2006

One of the most common operations in analytic query processing is the application of an aggregate... more One of the most common operations in analytic query processing is the application of an aggregate function to the result of a relational join. We describe an algorithm called the Sort-Merge-Shrink (SMS) Join for computing the answer to such a query over large, disk-based input tables. The key innovation of the SMS join is that if the input data are clustered in a statistically random fashion on disk, then at all times, the join provides an online, statistical estimator for the eventual answer to the query as well as probabilistic confidence bounds. Thus, a user can monitor the progress of the join throughout its execution and stop the join when satisfied with the estimate's accuracy or run the algorithm to completion with a total time requirement that is not much longer than that of other common join algorithms. This contrasts with other online join algorithms, which either do not offer such statistical guarantees or can only offer guarantees so long as the input data can fit into main memory.

Geometric Analysis of Continuous, Planar Shapes

Lecture Notes in Computer Science, 2003

We propose two differential geometric representations of planar shapes using: (i) direction funct... more We propose two differential geometric representations of planar shapes using: (i) direction functions and (ii) curvature functions, of their boundaries. Under either representation, planar shapes are treated as elements of infinite-dimensional shape spaces. Pairwise differences between the shapes are quantified using the lengths of geodesics connecting them on the shape spaces. We specify the geometry of the two shape spaces and utilize numerical methods for finding geodesics on them. Some applications of this shape analysis are illustrated including: (i) interpolation between shapes, (ii) clustering of objects according to their shapes, and (iii) computation of intrinsic mean shapes.

Modeling Dynamic Cellular Morphology in Images

Lecture Notes in Computer Science, 2012

This paper presents a geometric method for modeling dynamic features of cells in image sequences.... more This paper presents a geometric method for modeling dynamic features of cells in image sequences. The morphological changes in cellular membrane boundaries are represented as sequences of parameterized contours. These sequences are analyzed as paths on a shape space equipped with an invariant metric, and matched using dynamic time warping. Experimental results show high sensitivity of the proposed dynamic features to the morphological changes observed in lymphocytes of healthy mice after undergoing skin transplantation when compared with standard representation methods and shape features.

Riemannian Structures on Shape Spaces: A Framework for Statistical Inferences

Modeling and Simulation in Science, Engineering and Technology, 2006

Summary. Shape features are becoming increasingly important for inferences in image analysis. Sha... more

Elastic Shape Models for Interpolations of Curves in Image Sequences

Lecture Notes in Computer Science, 2005

Many applications in image analysis are concerned with the temporal evolution of shapes in video ... more Many applications in image analysis are concerned with the temporal evolution of shapes in video sequences. In situations involving low-contrast, low-quality images, human aid is often needed to extract shapes from images. An interesting approach is to use expert help to extract shapes in certain well-separated frames, and to use automated methods to extract shapes from intermediate frames. We present a technique to interpolate between expert generated shapes. This technique preserves salient features in the interpolated shapes, and allows analysts to model a continuous evolution of shapes, instead of a coarse sampling generated by the expert. The basic idea is to establish a correspondence between points on the two end shapes, and to construct a geodesic flow on a shape space maintaining that correspondence. This technique is demonstrated using echocardiagraphic images and infrared human gait sequences.

A Novel Representation for Riemannian Analysis of Elastic Curves in Rn

2007 IEEE Conference on Computer Vision and Pattern Recognition, 2007

We propose a novel representation of continuous, closed curves in ℝ(n) that is quite efficient fo... more We propose a novel representation of continuous, closed curves in ℝ(n) that is quite efficient for analyzing their shapes. We combine the strengths of two important ideas - elastic shape metric and path-straightening methods -in shape analysis and present a fast algorithm for finding geodesics in shape spaces. The elastic metric allows for optimal matching of features while path-straightening provides geodesics between curves. Efficiency results from the fact that the elastic metric becomes the simple (2) metric in the proposed representation. We present step-by-step algorithms for computing geodesics in this framework, and demonstrate them with 2-D as well as 3-D examples.

Applications of Shape-Distance Metric to Clustering Shape-Databases

Nonconvex Optimization and Its Applications, 2006

Summary. Based upon the geometric approach to clustering outlined in [KSMJ04], this paper present... more

Hierarchical Organization of Shapes for Efficient Retrieval

Lecture Notes in Computer Science, 2004

This paper presents a geometric approach to perform: (i) hierarchical clustering of imaged object... more This paper presents a geometric approach to perform: (i) hierarchical clustering of imaged objects according to the shapes of their boundaries, and (ii) testing of observed shapes for classification. An intrinsic metric on nonlinear, infinite-dimensional shape space, obtained using geodesic lengths, is used for clustering. This analysis is landmark free, does not require embedding shapes in R 2 , and uses ordinary differential equations for flows (as opposed to partial differential equations). Intrinsic analysis also leads to well defined shape statistics such as means and covariances, and is computationally efficient. Clustering is performed in a hierarchical fashion. At any level of hierarchy clusters are generated using a minimum dispersion criterion and an MCMC-type search algorithm. Cluster means become elements to be clustered at the next level. Gaussian models on tangent spaces are used to pose binary or multiple hypothesis tests for classifying observed shapes. Hierarchical clustering and shape testing combine to form an efficient tool for shape retrieval from a large database of shapes. For databases with n shapes, the searches are performed using log(n) tests on average. Examples are presented for demonstrating these tools using shapes from Kimia shape database and the Surrey fish database.

Shape Estimation and Object Classification in Images Using Geometric Priors

2006 Fortieth Asilomar Conference on Signals, Systems and Computers, 2006

Page 1. Shape Estimation and Object Classification in Images Using Geometric Priors Shantanu H. J... more

Modeling spatial patterns of shapes

2008 15th IEEE International Conference on Image Processing, 2008

We introduce a framework for modeling spatial patterns of shapes formed by multiple objects in an... more We introduce a framework for modeling spatial patterns of shapes formed by multiple objects in an image. Our approach is graph-based where each node denotes an object and attributes of a node consist of that object&amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;#39;s shape, position, orientation, and scale. Neighboring node are connected by edges, and they are allowed to interact in terms of their attributes/features. Similar to a Markov random field, but now applied to more sophisticated features space, the interactions are governed by energy functionals that can be internal or external. The internal energies, composed entirely of interactions between nodes, may include similarity between shapes and pose. The external energies, composed of outside influences, may include the data-likelihood term and the a-priori information about the shapes and the locations of the objects.

Applications of planar shape analysis to image-based inferences

International Conference on Acoustics, Speech, and Signal Processing, 2005

We describe an approach for statistical analysis of shapes of closed curves using tools from diff... more We describe an approach for statistical analysis of shapes of closed curves using tools from differential geometry. This approach uses geodesic paths to define a metric on shape space, that is used to compare shapes, to compute intrinsic statistics for a set of shapes, and to define probability models on shape spaces. We demonstrate this approach using: (i) interpolation of heart-wall boundaries in echocardiographic image sequences; and (ii) a study of shapes of human silhouettes in infrared surveillance images.

Riemannian Structures on Shape Spaces: A Framework for Statistical Inferences

Shape features are becoming increasingly important for inferences in image analysis. Shape analys... more Shape features are becoming increasingly important for inferences in image analysis. Shape analysis involves choosing mathematical representations of shapes, deriving tools for quantifying shape differences, and characterizing imaged objects according to the shapes of their boundaries. In this paper, we focus on characterizing shapes of continuous curves, both open and closed, in ℝ2. Under appropriate constraints that remove shape-preserving transformations, these curves form infinite-dimensional, non-linear spaces, called shape spaces, on which inferences are posed. We impose two Riemannian metrics on these spaces and study properties of the resulting structures. An important tool in Riemannian analysis of shapes is the construction of geodesic paths in shape spaces. Not only do the geodesics quantify shape differences, but they also provide a framework for computing intrinsic shape statistics. We will present algorithms to compute simple shape statistics — means and covariances — and will derive probability models on shape spaces using local principal component analysis (PCA), called tangent PCA (TPCA). These concepts are demonstrated using a number of applications: (i) unsupervised clustering of imaged objects according to their shapes, (ii) developing statistical shape models of human silhouettes in infrared surveillance images, (iii) interpolation of endo-and epicardial boundaries in echocardiographic image sequences, and (iv) using shape statistics to test phylogenetic hypotheses.

Robust Stratified Sampling Plans for Low Selectivity Queries

International Conference on Data Engineering, 2008

We consider the problem of estimating the result of an aggregate query with a very low selectivit... more We consider the problem of estimating the result of an aggregate query with a very low selectivity. Traditional sampling techniques can be ineffective for such a problem since a small random sample is likely to miss most or even all of the records satisfying the restrictive selection predicate. Stratfied sampling is useful in this situation, but a key problem in applying stratified sampling effectively is identifying which strata are important and developing a sampling plan that favors those strata in a robust fashion. We develop a solution to this problem that combines any prior knowledge or expectation about the stratification with information obtained from pilot sampling in a principled Bayesian framework.

Online Estimation For Subset-Based SQL Queries

Very Large Data Bases, 2005

The largest databases in use today are so large that answering a query exactly can take minutes, ... more The largest databases in use today are so large that answering a query exactly can take minutes, hours, or even days. One way to address this problem is to make use of approximation algorithms. Previous work on online aggregation has considered how to give online estimates with everincreasing accuracy for aggregate functions over relational join and selection queries. However, no existing work is applicable to online estimation over subset-based SQL queries-those queries with a correlated subquery linked to an outer query via a NOT EXISTS, NOT IN, EXISTS, or IN clause (other queries such as EXCEPT and INTERSECT can also be seen as subset-based queries). In this paper we develop algorithms for online estimation over such queries, and consider the difficult problem of providing probabilistic accuracy guarantees at all times during query execution.

A disk-based join with probabilistic guarantees

Proceedings of the 2005 ACM SIGMOD international conference on Management of data - SIGMOD '05, 2005

One of the most common operations in analytic query processing is the application of an aggregate... more One of the most common operations in analytic query processing is the application of an aggregate function to the result of a relational join. We describe an algorithm for computing the answer to such a query over large, disk-based input tables. The key innovation of our algorithm is that at all times, it provides an online, statistical estimator for the eventual answer to the query, as well as probabilistic confidence bounds. Thus, a user can monitor the progress of the join throughout its execution and stop the join when satisfied with the estimate's accuracy, or run the algorithm to completion with a total time requirement that is not much longer than other common join algorithms. This contrasts with other online join algorithms, which either do not offer such statistical guarantees or can only offer guarantees so long as the input data can fit into core memory.

Robust Stratified Sampling Plans for Low Selectivity Queries

2008 IEEE 24th International Conference on Data Engineering, 2008

We consider the problem of estimating the result of an aggregate query with a very low selectivit... more We consider the problem of estimating the result of an aggregate query with a very low selectivity. Traditional sampling techniques can be ineffective for such a problem since a small random sample is likely to miss most or even all of the records satisfying the restrictive selection predicate. Stratfied sampling is useful in this situation, but a key problem in applying stratified sampling effectively is identifying which strata are important and developing a sampling plan that favors those strata in a robust fashion. We develop a solution to this problem that combines any prior knowledge or expectation about the stratification with information obtained from pilot sampling in a principled Bayesian framework.

The Sort-Merge-Shrink join

ACM Transactions on Database Systems, 2006

One of the most common operations in analytic query processing is the application of an aggregate... more One of the most common operations in analytic query processing is the application of an aggregate function to the result of a relational join. We describe an algorithm called the Sort-Merge-Shrink (SMS) Join for computing the answer to such a query over large, disk-based input tables. The key innovation of the SMS join is that if the input data are clustered in a statistically random fashion on disk, then at all times, the join provides an online, statistical estimator for the eventual answer to the query as well as probabilistic confidence bounds. Thus, a user can monitor the progress of the join throughout its execution and stop the join when satisfied with the estimate's accuracy or run the algorithm to completion with a total time requirement that is not much longer than that of other common join algorithms. This contrasts with other online join algorithms, which either do not offer such statistical guarantees or can only offer guarantees so long as the input data can fit into main memory.

A disk-based join with probabilistic guarantees

International Conference on Management of Data, 2005

One of the most common operations in analytic query processing is the application of an aggregate... more One of the most common operations in analytic query processing is the application of an aggregate function to the result of a relational join. We describe an algorithm for computing the answer to such a query over large, disk-based input tables. The key innovation of our algorithm is that at all times, it provides an online, statistical estimator for the eventual answer to the query, as well as probabilistic confidence bounds. Thus, a user can monitor the progress of the join throughout its execution and stop the join when satisfied with the estimate's accuracy, or run the algorithm to completion with a total time requirement that is not much longer than other common join algorithms. This contrasts with other online join algorithms, which either do not offer such statistical guarantees or can only offer guarantees so long as the input data can fit into core memory.

Oracle real application testing

International Conference on Management of Data, 2008

This paper presents the Oracle solution for database testing delivered in the Oracle 11g Database... more

Materialized sample views for database approximation

Knowledge and Data Engineering, IEEE …, 2008

We consider the problem of creating a sample view of a database table. A sample view is an indexe... more We consider the problem of creating a sample view of a database table. A sample view is an indexed, materialized view that permits efficient sampling from an arbitrary range query over the view. Such "sample views" are very useful to applications that require random samples from a database: approximate query processing, online aggregation, data mining, and randomized algorithms are a few examples. Our core technical contribution is a new file organization called the ACE Tree that is suitable for organizing and indexing a sample view. One of the most important aspects of the ACE Tree is that it supports online random sampling from the view. That is, at all times, the set of records returned by the ACE Tree constitutes a statistically random sample of the database records satisfying the relational selection predicate over the view. Our paper presents experimental results that demonstrate the utility of the ACE Tree.

The Sort-Merge-Shrink join

ACM Transactions on Database Systems, 2006

One of the most common operations in analytic query processing is the application of an aggregate... more One of the most common operations in analytic query processing is the application of an aggregate function to the result of a relational join. We describe an algorithm called the Sort-Merge-Shrink (SMS) Join for computing the answer to such a query over large, disk-based input tables. The key innovation of the SMS join is that if the input data are clustered in a statistically random fashion on disk, then at all times, the join provides an online, statistical estimator for the eventual answer to the query as well as probabilistic confidence bounds. Thus, a user can monitor the progress of the join throughout its execution and stop the join when satisfied with the estimate's accuracy or run the algorithm to completion with a total time requirement that is not much longer than that of other common join algorithms. This contrasts with other online join algorithms, which either do not offer such statistical guarantees or can only offer guarantees so long as the input data can fit into main memory.

Geometric Analysis of Continuous, Planar Shapes

Lecture Notes in Computer Science, 2003

We propose two differential geometric representations of planar shapes using: (i) direction funct... more We propose two differential geometric representations of planar shapes using: (i) direction functions and (ii) curvature functions, of their boundaries. Under either representation, planar shapes are treated as elements of infinite-dimensional shape spaces. Pairwise differences between the shapes are quantified using the lengths of geodesics connecting them on the shape spaces. We specify the geometry of the two shape spaces and utilize numerical methods for finding geodesics on them. Some applications of this shape analysis are illustrated including: (i) interpolation between shapes, (ii) clustering of objects according to their shapes, and (iii) computation of intrinsic mean shapes.

Modeling Dynamic Cellular Morphology in Images

Lecture Notes in Computer Science, 2012

This paper presents a geometric method for modeling dynamic features of cells in image sequences.... more This paper presents a geometric method for modeling dynamic features of cells in image sequences. The morphological changes in cellular membrane boundaries are represented as sequences of parameterized contours. These sequences are analyzed as paths on a shape space equipped with an invariant metric, and matched using dynamic time warping. Experimental results show high sensitivity of the proposed dynamic features to the morphological changes observed in lymphocytes of healthy mice after undergoing skin transplantation when compared with standard representation methods and shape features.

Riemannian Structures on Shape Spaces: A Framework for Statistical Inferences

Modeling and Simulation in Science, Engineering and Technology, 2006

Summary. Shape features are becoming increasingly important for inferences in image analysis. Sha... more

Elastic Shape Models for Interpolations of Curves in Image Sequences

Lecture Notes in Computer Science, 2005

Many applications in image analysis are concerned with the temporal evolution of shapes in video ... more Many applications in image analysis are concerned with the temporal evolution of shapes in video sequences. In situations involving low-contrast, low-quality images, human aid is often needed to extract shapes from images. An interesting approach is to use expert help to extract shapes in certain well-separated frames, and to use automated methods to extract shapes from intermediate frames. We present a technique to interpolate between expert generated shapes. This technique preserves salient features in the interpolated shapes, and allows analysts to model a continuous evolution of shapes, instead of a coarse sampling generated by the expert. The basic idea is to establish a correspondence between points on the two end shapes, and to construct a geodesic flow on a shape space maintaining that correspondence. This technique is demonstrated using echocardiagraphic images and infrared human gait sequences.

A Novel Representation for Riemannian Analysis of Elastic Curves in Rn

2007 IEEE Conference on Computer Vision and Pattern Recognition, 2007

We propose a novel representation of continuous, closed curves in ℝ(n) that is quite efficient fo... more We propose a novel representation of continuous, closed curves in ℝ(n) that is quite efficient for analyzing their shapes. We combine the strengths of two important ideas - elastic shape metric and path-straightening methods -in shape analysis and present a fast algorithm for finding geodesics in shape spaces. The elastic metric allows for optimal matching of features while path-straightening provides geodesics between curves. Efficiency results from the fact that the elastic metric becomes the simple (2) metric in the proposed representation. We present step-by-step algorithms for computing geodesics in this framework, and demonstrate them with 2-D as well as 3-D examples.

Applications of Shape-Distance Metric to Clustering Shape-Databases

Nonconvex Optimization and Its Applications, 2006

Summary. Based upon the geometric approach to clustering outlined in [KSMJ04], this paper present... more

Hierarchical Organization of Shapes for Efficient Retrieval

Lecture Notes in Computer Science, 2004

This paper presents a geometric approach to perform: (i) hierarchical clustering of imaged object... more This paper presents a geometric approach to perform: (i) hierarchical clustering of imaged objects according to the shapes of their boundaries, and (ii) testing of observed shapes for classification. An intrinsic metric on nonlinear, infinite-dimensional shape space, obtained using geodesic lengths, is used for clustering. This analysis is landmark free, does not require embedding shapes in R 2 , and uses ordinary differential equations for flows (as opposed to partial differential equations). Intrinsic analysis also leads to well defined shape statistics such as means and covariances, and is computationally efficient. Clustering is performed in a hierarchical fashion. At any level of hierarchy clusters are generated using a minimum dispersion criterion and an MCMC-type search algorithm. Cluster means become elements to be clustered at the next level. Gaussian models on tangent spaces are used to pose binary or multiple hypothesis tests for classifying observed shapes. Hierarchical clustering and shape testing combine to form an efficient tool for shape retrieval from a large database of shapes. For databases with n shapes, the searches are performed using log(n) tests on average. Examples are presented for demonstrating these tools using shapes from Kimia shape database and the Surrey fish database.

Shape Estimation and Object Classification in Images Using Geometric Priors

2006 Fortieth Asilomar Conference on Signals, Systems and Computers, 2006

Page 1. Shape Estimation and Object Classification in Images Using Geometric Priors Shantanu H. J... more

Modeling spatial patterns of shapes

2008 15th IEEE International Conference on Image Processing, 2008

We introduce a framework for modeling spatial patterns of shapes formed by multiple objects in an... more We introduce a framework for modeling spatial patterns of shapes formed by multiple objects in an image. Our approach is graph-based where each node denotes an object and attributes of a node consist of that object&amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;#39;s shape, position, orientation, and scale. Neighboring node are connected by edges, and they are allowed to interact in terms of their attributes/features. Similar to a Markov random field, but now applied to more sophisticated features space, the interactions are governed by energy functionals that can be internal or external. The internal energies, composed entirely of interactions between nodes, may include similarity between shapes and pose. The external energies, composed of outside influences, may include the data-likelihood term and the a-priori information about the shapes and the locations of the objects.

Applications of planar shape analysis to image-based inferences

International Conference on Acoustics, Speech, and Signal Processing, 2005

We describe an approach for statistical analysis of shapes of closed curves using tools from diff... more We describe an approach for statistical analysis of shapes of closed curves using tools from differential geometry. This approach uses geodesic paths to define a metric on shape space, that is used to compare shapes, to compute intrinsic statistics for a set of shapes, and to define probability models on shape spaces. We demonstrate this approach using: (i) interpolation of heart-wall boundaries in echocardiographic image sequences; and (ii) a study of shapes of human silhouettes in infrared surveillance images.

Riemannian Structures on Shape Spaces: A Framework for Statistical Inferences

Shape features are becoming increasingly important for inferences in image analysis. Shape analys... more Shape features are becoming increasingly important for inferences in image analysis. Shape analysis involves choosing mathematical representations of shapes, deriving tools for quantifying shape differences, and characterizing imaged objects according to the shapes of their boundaries. In this paper, we focus on characterizing shapes of continuous curves, both open and closed, in ℝ2. Under appropriate constraints that remove shape-preserving transformations, these curves form infinite-dimensional, non-linear spaces, called shape spaces, on which inferences are posed. We impose two Riemannian metrics on these spaces and study properties of the resulting structures. An important tool in Riemannian analysis of shapes is the construction of geodesic paths in shape spaces. Not only do the geodesics quantify shape differences, but they also provide a framework for computing intrinsic shape statistics. We will present algorithms to compute simple shape statistics — means and covariances — and will derive probability models on shape spaces using local principal component analysis (PCA), called tangent PCA (TPCA). These concepts are demonstrated using a number of applications: (i) unsupervised clustering of imaged objects according to their shapes, (ii) developing statistical shape models of human silhouettes in infrared surveillance images, (iii) interpolation of endo-and epicardial boundaries in echocardiographic image sequences, and (iv) using shape statistics to test phylogenetic hypotheses.