This work presents a geometry-based image retrieval approach for multi-object images. We commence with developing an effective shape matching method for closed boundaries. Then, a structured representation, called curvature tree (CT), is introduced to extend the shape matching approach to handle images containing multiple objects with possible holes. We also propose an algorithm, based on Gestalt principles, to detect and extract high-level boundaries (or envelopes), which may evolve as a result of the spatial arrangement of a group of image objects. At first, a shape retrieval method using triangle-area representation (TAR) is presented for non-rigid shapes with closed boundaries. This representation is effective in capturing both local and global characteristics of a shape, invariant to translation, rotation, scaling and shear, and robust against noise and moderate amounts of occlusion. For matching, two algorithms are introduced. The first algorithm matches concavity maxima points extracted from TAR image obtained by thresholding the TAR. In the second matching algorithm, dynamic space warping (DSW) is employed to search efficiently for the optimal (least cost) correspondence between the points of two shapes. Experimental results using the MPEG-7 CE-1 database of 1400 shapes show the superiority of our method over other recent methods. Then, a geometry-based image retrieval system is developed for multi-object images. We model both shape and topology of image objects including holes using a structured representation called curvature tree (CT). To facilitate shape-based matching, the TAR of each object and hole is stored at the corresponding node in the CT. The similarity between two CTs is measured based on the maximum similarity subtree isomorphism (MSSI) where a one-to-one correspondence is established between the nodes of the two trees. Our matching scheme agrees with many recent findings in psychology about the human perception of multi-object images. Two algorithms are introduced to solve the MSSI problem: an approximate and an exact. Both algorithms have polynomial-time computational complexity and use the DSW as the similarity measure between the attributed nodes. Experiments on a database of 13500 medical images and a database of 1580 logo images have shown the effectiveness of the proposed method. The purpose of the last part is to allow for high-level shape retrieval in multi-object images by detecting and extracting the envelope of high-level object groupings in the image. Motivated by studies in Gestalt theory, a new algorithm for the envelope extraction is proposed that works in two stages. The first stage detects the envelope (if exists) and groups its objects using hierarchical clustering. In the second stage, each grouping is merged using morphological operations and then further refined using concavity tree reconstruction to eliminate odd concavities in the extracted envelope. Experiment on a set of 110 logo images demonstrates the feasibility of our approach.

The recognition of 3-D objects from their silhouettes demands a shape representation which is invariant to minor changes in viewpoint and articulation. This invariance can be achieved by parsing a silhouette into parts and relationships that are stable across similar object views. Medial descriptions, such as skeletons and shock graphs, attempt to decompose a shape into parts, but suffer from instabilities that lead to similar shapes being represented by dissimilar part sets. We propose a novel shape parsing approach based on identifying and regularizing the ligature structure of a given medial axis. The result of this process is a bone graph, a new medial shape abstraction that captures a more intuitive notion of an object’s parts than a skeleton or a shock graph, and offers improved stability and within-class deformation invariance over the shock graph. The bone graph, unlike the shock graph, has attributed edges that specify how and where two medial parts meet. We propose a novel shape matching framework that exploits this relational information by formulating the problem as an inexact directed acyclic graph matching, and extending a leading bipartite graph-based matching framework introduced for matching shock graphs. In addition to accommodating the relational information, our new framework is better able to enforce hierarchical and sibling constraints between nodes, resulting in a more general and more powerful matching framework. We evaluate our matching framework with respect to a competing shock graph matching framework, and show that for the task of view-based object categorization, our matching framework applied to bone graphs outperforms the competing framework. Moreover, our matching framework applied to shock graphs also outperforms the competing shock graph matching algorithm, demonstrating the generality and improved performance of our matching algorithm.

The recognition of 3-D objects from their silhouettes demands a shape representation which is invariant to minor changes in viewpoint and articulation. This invariance can be achieved by parsing a silhouette into parts and relationships that are stable across similar object views. Medial descriptions, such as skeletons and shock graphs, attempt to decompose a shape into parts, but suffer from instabilities that lead to similar shapes being represented by dissimilar part sets. We propose a novel shape parsing approach based on identifying and regularizing the ligature structure of a given medial axis. The result of this process is a bone graph, a new medial shape abstraction that captures a more intuitive notion of an object’s parts than a skeleton or a shock graph, and offers improved stability and within-class deformation invariance over the shock graph. The bone graph, unlike the shock graph, has attributed edges that specify how and where two medial parts meet. We propose a novel shape matching framework that exploits this relational information by formulating the problem as an inexact directed acyclic graph matching, and extending a leading bipartite graph-based matching framework introduced for matching shock graphs. In addition to accommodating the relational information, our new framework is better able to enforce hierarchical and sibling constraints between nodes, resulting in a more general and more powerful matching framework. We evaluate our matching framework with respect to a competing shock graph matching framework, and show that for the task of view-based object categorization, our matching framework applied to bone graphs outperforms the competing framework. Moreover, our matching framework applied to shock graphs also outperforms the competing shock graph matching algorithm, demonstrating the generality and improved performance of our matching algorithm.

This work presents a geometry-based image retrieval approach for multi-object images. We commence with developing an effective shape matching method for closed boundaries. Then, a structured representation, called curvature tree (CT), is introduced to extend the shape matching approach to handle images containing multiple objects with possible holes. We also propose an algorithm, based on Gestalt principles, to detect and extract high-level boundaries (or envelopes), which may evolve as a result of the spatial arrangement of a group of image objects. At first, a shape retrieval method using triangle-area representation (TAR) is presented for non-rigid shapes with closed boundaries. This representation is effective in capturing both local and global characteristics of a shape, invariant to translation, rotation, scaling and shear, and robust against noise and moderate amounts of occlusion. For matching, two algorithms are introduced. The first algorithm matches concavity maxima points extracted from TAR image obtained by thresholding the TAR. In the second matching algorithm, dynamic space warping (DSW) is employed to search efficiently for the optimal (least cost) correspondence between the points of two shapes. Experimental results using the MPEG-7 CE-1 database of 1400 shapes show the superiority of our method over other recent methods. Then, a geometry-based image retrieval system is developed for multi-object images. We model both shape and topology of image objects including holes using a structured representation called curvature tree (CT). To facilitate shape-based matching, the TAR of each object and hole is stored at the corresponding node in the CT. The similarity between two CTs is measured based on the maximum similarity subtree isomorphism (MSSI) where a one-to-one correspondence is established between the nodes of the two trees. Our matching scheme agrees with many recent findings in psychology about the human perception of multi-object images. Two algorithms are introduced to solve the MSSI problem: an approximate and an exact. Both algorithms have polynomial-time computational complexity and use the DSW as the similarity measure between the attributed nodes. Experiments on a database of 13500 medical images and a database of 1580 logo images have shown the effectiveness of the proposed method. The purpose of the last part is to allow for high-level shape retrieval in multi-object images by detecting and extracting the envelope of high-level object groupings in the image. Motivated by studies in Gestalt theory, a new algorithm for the envelope extraction is proposed that works in two stages. The first stage detects the envelope (if exists) and groups its objects using hierarchical clustering. In the second stage, each grouping is merged using morphological operations and then further refined using concavity tree reconstruction to eliminate odd concavities in the extracted envelope. Experiment on a set of 110 logo images demonstrates the feasibility of our approach.

The segmentation of medical images is a difficult task due to the inhomogeneous intensity variations that occurs during digital image acquisition, the complicated shape of the object, and the medical expert’s lack of semantic knowledge. Automated segmentation algorithms work well for some medical images, but no algorithm has been general enough to work for all medical images. In practice, most of the time the segmentation results are corrected by the experts before the actual use. In this work, we are motivated to determine how to make use of manually segmented data in automatic segmentation. The key idea is to transfer the ground truth segmentation from the database of train images to a given test image. The ground truth segmentation of MR images is done by experts. The process includes a hierarchical image decomposition approach that performs the shape matching of test images at several levels, starting with the image as a whole (i.e. level 0) and then going through a pyramid decomposition (i.e. level 1, level 2, etc.) with the database of the train images and the given test image. The goal of pyramid decomposition is to find the section of the training image that best matches a section of the test image of a different level. After that, a re-composition approach is taken to place the best matched sections of the training image to the original test image space. Finally, the ground truth segmentation is transferred from the best training images to their corresponding location in the test image. We have tested our method on a hip joint MR image database and the experiment shows successful results on level 0, level 1 and level 2 re-compositions. Results improve with deeper level decompositions, which supports our hypotheses.

While computational fluid dynamics (CFD) simulations are an indispensable tool in modern aerospace engineering design, they bear a severe computational burden in applications where simulation results must be found quickly or repeatedly. Therefore, creating computationally inexpensive models that can capture complex fluid behaviors is a long-sought-after goal. As a result, methods to construct these reduced order models (ROMs) have seen increasing research interest. Still, parameter dependent high-speed flows that contain shock waves are a particularly challenging class of problems that introduces many complications in ROM frameworks. To make approximations in a linear space, ROM techniques for these problems require that basis functions are transformed such that discontinuities are aligned into a consistent reference frame. Techniques to construct these transformations, however, fail when the topology of shocks is not consistent between data snapshots. In this work, we first identify key features of these topology changes, and how that constrains transformations of this kind. We then construct a new modeling framework that can effectively deal with shockwave interactions that are known to cause failures. The capabilities of the resulting model were evaluated by analyzing supersonic flows over a wedge and a forward-facing step. In the case of the forward-facing step, when shock topology changes with Mach number, our method exhibits significant accuracy improvements. Suggestions for further developments and improvements to our methodology are also identified and discussed / Master of Science / While computational fluid dynamics (CFD) simulations are an indispensable tool in modern aerospace engineering design, they bear a severe computational burden in applications where simulation results must be found quickly or repeatedly. Therefore, creating computationally inexpensive models that can capture complex fluid behaviors is a long-sought-after goal. As a result, methods to construct these reduced order models (ROMs) have seen increasing research interest. Still, high-speed flows that contain shock waves are a particularly challenging class of problems that introduces many complications in ROM frameworks. First, we identify some of the common failure modes in previous ROM methodologies. We then construct a new modeling framework that can effectively deal with shockwave interactions that are known to cause these failures. The capabilities of the resulting model were evaluated by analyzing supersonic flows over a wedge and a forward-facing step. In cases where previous modeling frameworks are known to fail, our method exhibits significant accuracy improvements. Suggestions for further developments and improvements to our methodology are also identified and discussed.

Proteins and the formation of large protein complexes are essential parts of living organisms. Proteins are present in all aspects of life processes, performing a multitude of various functions ranging from being structural components of cells, to facilitating the passage of certain molecules between various regions of cells. The 'protein docking problem' refers to the computational method of predicting the appropriate matching pair of a protein (receptor) with respect to another protein (ligand), when attempting to bind to one another to form a stable complex. Research shows that matching the three-dimensional (3D) geometric structures of candidate proteins plays a key role in determining a so-called docking pair, which is one of the key aspects of the Computer Aided Drug Design process. However, the active sites which are responsible for binding do not always present a rigid-body shape matching problem. Rather, they may undergo sufficient deformation when docking occurs, which complicates the problem of finding a match. To address this issue, we present an isometry-invariant and topologically robust partial shape matching method for finding complementary protein binding sites, which we call the ProtoDock algorithm. The ProtoDock algorithm comes in two variations. The first version performs a partial shape complementarity matching by initially segmenting the underlying protein object mesh into smaller portions using a spectral mesh segmentation approach. The Heat Kernel Signature (HKS), the underlying basis of our shape descriptor, is subsequently computed for the obtained segments. A final descriptor vector is constructed from the Heat Kernel Signatures and used as the basis for the segment matching. The three different descriptor methods employed are, the accepted Bag of Features (BoF) technique, and our two novel approaches, Closest Medoid Set (CMS) and Medoid Set Average (MSA). The second variation of our ProtoDock algorithm aims to perform the partial matching by utilizing the pointwise HKS descriptors. The use of the pointwise HKS is mainly motivated by the suggestion that, at adequate times, the Heat Kernel Signature of a point on a surface sufficiently describes its neighbourhood. Hence, the HKS of a point may serve as the representative descriptor of its given region of which it forms a part. We propose three (3) sampling methods---Uniform, Random, and Segment-based Random sampling---for selecting these points for the partial matching. Random and Segment-based Random sampling both prove superior to the Uniform sampling method. Our experimental results, run against the Protein-Protein Benchmark 4.0, demonstrate the viability of our approach, in that, it successfully returns known binding segments for known pairing proteins. Furthermore, our ProtoDock-1 algorithm still still yields good results for low resolution protein meshes. This results in even faster processing and matching times with sufficiently reduced computational requirements when obtaining the HKS.

Proteins and the formation of large protein complexes are essential parts of living organisms. Proteins are present in all aspects of life processes, performing a multitude of various functions ranging from being structural components of cells, to facilitating the passage of certain molecules between various regions of cells. The 'protein docking problem' refers to the computational method of predicting the appropriate matching pair of a protein (receptor) with respect to another protein (ligand), when attempting to bind to one another to form a stable complex. Research shows that matching the three-dimensional (3D) geometric structures of candidate proteins plays a key role in determining a so-called docking pair, which is one of the key aspects of the Computer Aided Drug Design process. However, the active sites which are responsible for binding do not always present a rigid-body shape matching problem. Rather, they may undergo sufficient deformation when docking occurs, which complicates the problem of finding a match. To address this issue, we present an isometry-invariant and topologically robust partial shape matching method for finding complementary protein binding sites, which we call the ProtoDock algorithm. The ProtoDock algorithm comes in two variations. The first version performs a partial shape complementarity matching by initially segmenting the underlying protein object mesh into smaller portions using a spectral mesh segmentation approach. The Heat Kernel Signature (HKS), the underlying basis of our shape descriptor, is subsequently computed for the obtained segments. A final descriptor vector is constructed from the Heat Kernel Signatures and used as the basis for the segment matching. The three different descriptor methods employed are, the accepted Bag of Features (BoF) technique, and our two novel approaches, Closest Medoid Set (CMS) and Medoid Set Average (MSA). The second variation of our ProtoDock algorithm aims to perform the partial matching by utilizing the pointwise HKS descriptors. The use of the pointwise HKS is mainly motivated by the suggestion that, at adequate times, the Heat Kernel Signature of a point on a surface sufficiently describes its neighbourhood. Hence, the HKS of a point may serve as the representative descriptor of its given region of which it forms a part. We propose three (3) sampling methods---Uniform, Random, and Segment-based Random sampling---for selecting these points for the partial matching. Random and Segment-based Random sampling both prove superior to the Uniform sampling method. Our experimental results, run against the Protein-Protein Benchmark 4.0, demonstrate the viability of our approach, in that, it successfully returns known binding segments for known pairing proteins. Furthermore, our ProtoDock-1 algorithm still still yields good results for low resolution protein meshes. This results in even faster processing and matching times with sufficiently reduced computational requirements when obtaining the HKS.

Weighted graph matching is a good way to align a pair of shapes represented by a set of descriptive local features; the set of correspondences produced by the minimum cost of matching features from one shape to the features of the other often reveals how similar the two shapes are. However, due to the complexity of computing the exact minimum cost matching, previous algorithms could only run efficiently when using a limited number of features per shape, and could not scale to perform retrievals from large databases. We present a contour matching algorithm that quickly computes the minimum weight matching between sets of descriptive local features using a recently introduced low-distortion embedding of the Earth Mover's Distance (EMD) into a normed space. Given a novel embedded contour, the nearest neighbors in a database of embedded contours are retrieved in sublinear time via approximate nearest neighbors search. We demonstrate our shape matching method on databases of 10,000 images of human figures and 60,000 images of handwritten digits.

Weighted graph matching is a good way to align a pair of shapesrepresented by a set of descriptive local features; the set ofcorrespondences produced by the minimum cost of matching features fromone shape to the features of the other often reveals how similar thetwo shapes are. However, due to the complexity of computing the exactminimum cost matching, previous algorithms could only run efficientlywhen using a limited number of features per shape, and could not scaleto perform retrievals from large databases. We present a contourmatching algorithm that quickly computes the minimum weight matchingbetween sets of descriptive local features using a recently introducedlow-distortion embedding of the Earth Mover's Distance (EMD) into anormed space. Given a novel embedded contour, the nearest neighborsin a database of embedded contours are retrieved in sublinear time viaapproximate nearest neighbors search. We demonstrate our shapematching method on databases of 10,000 images of human figures and60,000 images of handwritten digits.