The eccentricity transform associates to each point of a shape the distance to the point farthest... more The eccentricity transform associates to each point of a shape the distance to the point farthest away from it. The transform is defined in any dimension, for open and closed manyfolds, is robust to Salt & Pepper noise, and is quasi-invariant to articulated motion. This paper presents and algorithm to efficiently compute the eccentricity transform of a polygonal shape with or without holes. In particular, based on existing and new properties, we provide an algorithm to decompose a polygon using parallel steps, and use the result to derive the eccentricity value of any point.
How do we bridge the representational gap between image features and coarse model features? is ... more How do we bridge the representational gap between image features and coarse model features? is the question asked by the authors of [1] when referring to several contemporary research issues. They identify the one-to-one correspondence between salient image ...
A concept relating story-board description of video sequences with spatio-temporal hierarchies bu... more A concept relating story-board description of video sequences with spatio-temporal hierarchies build by local contraction processes of spatio-temporal relations is presented. Object trajectories are curves in which their ends and junctions are identified. Junction points happen when two (or more) trajectories touch or cross each other, which we interpret as the “interaction” of two objects. Trajectory connections are interpreted as the high level descriptions.
Structural pattern recognition describes and classifies data based on the relationships of featur... more Structural pattern recognition describes and classifies data based on the relationships of features and parts. Topological invariants, like the Euler number, characterize the structure of objects of any dimension. Cohomology can provide more refined algebraic invariants to a topological space than does homology. It assigns ‘quantities’ to the chains used in homology to characterize holes of any dimension. Graph pyramids can be used to describe subdivisions of the same object at multiple levels of detail. This paper presents cohomology in the context of structural pattern recognition and introduces an algorithm to efficiently compute representative cocycles (the basic elements of cohomology) in 2D using a graph pyramid. Extension to nD and application in the context of pattern recognition are discussed.
The authors in [6] suggest to bridge and not to elimi-nate the representational gap, and to focus... more The authors in [6] suggest to bridge and not to elimi-nate the representational gap, and to focus efforts on re-gion segmentation, perceptual grouping, and image abstrac-tion. Hence, evaluation of segmentations by different algo-rithms is also an effort worthy of concentrating. The ...
The eccentricity transform associates to each point of a shape the geodesic distance to the point... more The eccentricity transform associates to each point of a shape the geodesic distance to the point farthest away from it. The transform is defined in any dimension, for simply and non simply connected sets. It is robust to Salt & Pepper noise and is quasi-invariant to articulated motion. Discrete analytical concentric circles with constant thickness and increasing radius pave the 2D plane. An ordering between pixels belonging to circles with different radius is created that enables the tracking of a wavefront moving away from the circle center. This is used to efficiently compute the single source shape bounded distance transform which in turn is used to compute the eccentricity transform. Experimental results for three algorithms are given: a novel one, an existing one, and a refined version of the existing one. They show a good speed/error compromise.
Eccentricity measures the shortest length of the paths from a given vertex v to reach any other v... more Eccentricity measures the shortest length of the paths from a given vertex v to reach any other vertex w of a connected graph. Computed for every vertex v it transforms the connectivity structure of the graph into a set of values. For a connected region of a digital image it is defined through its neighbourhood graph and the given metric. This transform assigns to each element of a region a value that depends on it’s location inside the region and the region’s shape. The definition and several properties are given. Presented experimental results verify its robustness against noise, and its increased stability compared to the distance transform. Future work will include using it for shape decomposition, representation, and matching.
This paper presents an approach to extract the rigid parts of an observed articulated object. Fir... more This paper presents an approach to extract the rigid parts of an observed articulated object. First, a spatio-temporal filtering in a video selects interest points that correspond to rigid parts. This selection is driven by the spatial relationships and the movement of the interest points. Then, a graph pyramid is built, guided by the orientation changes of the object parts in the scene. This leads to a decomposition of the scene into its rigid parts. Each vertex in the top level of the pyramid represents one rigid part in the scene.
Structural pattern recognition describes and classifies data based on the relationships of featur... more Structural pattern recognition describes and classifies data based on the relationships of features and parts. Topological invariants, like the Euler number, characterize the structure of objects of any dimension. Cohomology can provide more refined algebraic invariants to a topological space than does homology. It assigns ‘quantities’ to the chains used in homology to characterize holes of any dimension. Graph pyramids can be used to describe subdivisions of the same object at multiple levels of detail. This paper presents cohomology in the context of structural pattern recognition and introduces an algorithm to efficiently compute representative cocycles (the basic elements of cohomology) in 2D using a graph pyramid. Extension to nD and application in the context of pattern recognition are discussed.
In this paper we use different decimation strategies in irregular pyramid segmentation framework,... more In this paper we use different decimation strategies in irregular pyramid segmentation framework, to produce perceptually important groupings. These graph decimation strategies, based on the maximum independent set concept, used in Borůvka’s minimum spanning tree based partitioning method, show similar discrepancy segmentation errors. Global and local consistency error measures do not show big differences between the methods although human visual inspection of the results show advantages for one method. To a certain extent this subjective impression is captured by the new criteria of ’region size variation’.
We introduce a method for computing homology groups and their generators of a 2D image, using a h... more We introduce a method for computing homology groups and their generators of a 2D image, using a hierarchical structure i.e. irregular graph pyramid. Starting from an image, a hierarchy of the image is built, by two operations that preserve homology of each region. Instead of computing homology generators in the base where the number of entities (cells) is large, we first reduce the number of cells by a graph pyramid. Then homology generators are computed efficiently on the top level of the pyramid, since the number of cells is small, and a top down process is then used to deduce homology generators in any level of the pyramid, including the base level i.e. the initial image. We show that the new method produces valid homology generators and present some experimental results.
The eccentricity transform associates to each point of a shape the distance to the point farthest... more The eccentricity transform associates to each point of a shape the distance to the point farthest away from it. The transform is defined in any dimension, for open and closed manyfolds, is robust to Salt & Pepper noise, and is quasi-invariant to articulated motion. This paper presents and algorithm to efficiently compute the eccentricity transform of a polygonal shape with or without holes. In particular, based on existing and new properties, we provide an algorithm to decompose a polygon using parallel steps, and use the result to derive the eccentricity value of any point.
How do we bridge the representational gap between image features and coarse model features? is ... more How do we bridge the representational gap between image features and coarse model features? is the question asked by the authors of [1] when referring to several contemporary research issues. They identify the one-to-one correspondence between salient image ...
A concept relating story-board description of video sequences with spatio-temporal hierarchies bu... more A concept relating story-board description of video sequences with spatio-temporal hierarchies build by local contraction processes of spatio-temporal relations is presented. Object trajectories are curves in which their ends and junctions are identified. Junction points happen when two (or more) trajectories touch or cross each other, which we interpret as the “interaction” of two objects. Trajectory connections are interpreted as the high level descriptions.
Structural pattern recognition describes and classifies data based on the relationships of featur... more Structural pattern recognition describes and classifies data based on the relationships of features and parts. Topological invariants, like the Euler number, characterize the structure of objects of any dimension. Cohomology can provide more refined algebraic invariants to a topological space than does homology. It assigns ‘quantities’ to the chains used in homology to characterize holes of any dimension. Graph pyramids can be used to describe subdivisions of the same object at multiple levels of detail. This paper presents cohomology in the context of structural pattern recognition and introduces an algorithm to efficiently compute representative cocycles (the basic elements of cohomology) in 2D using a graph pyramid. Extension to nD and application in the context of pattern recognition are discussed.
The authors in [6] suggest to bridge and not to elimi-nate the representational gap, and to focus... more The authors in [6] suggest to bridge and not to elimi-nate the representational gap, and to focus efforts on re-gion segmentation, perceptual grouping, and image abstrac-tion. Hence, evaluation of segmentations by different algo-rithms is also an effort worthy of concentrating. The ...
The eccentricity transform associates to each point of a shape the geodesic distance to the point... more The eccentricity transform associates to each point of a shape the geodesic distance to the point farthest away from it. The transform is defined in any dimension, for simply and non simply connected sets. It is robust to Salt & Pepper noise and is quasi-invariant to articulated motion. Discrete analytical concentric circles with constant thickness and increasing radius pave the 2D plane. An ordering between pixels belonging to circles with different radius is created that enables the tracking of a wavefront moving away from the circle center. This is used to efficiently compute the single source shape bounded distance transform which in turn is used to compute the eccentricity transform. Experimental results for three algorithms are given: a novel one, an existing one, and a refined version of the existing one. They show a good speed/error compromise.
Eccentricity measures the shortest length of the paths from a given vertex v to reach any other v... more Eccentricity measures the shortest length of the paths from a given vertex v to reach any other vertex w of a connected graph. Computed for every vertex v it transforms the connectivity structure of the graph into a set of values. For a connected region of a digital image it is defined through its neighbourhood graph and the given metric. This transform assigns to each element of a region a value that depends on it’s location inside the region and the region’s shape. The definition and several properties are given. Presented experimental results verify its robustness against noise, and its increased stability compared to the distance transform. Future work will include using it for shape decomposition, representation, and matching.
This paper presents an approach to extract the rigid parts of an observed articulated object. Fir... more This paper presents an approach to extract the rigid parts of an observed articulated object. First, a spatio-temporal filtering in a video selects interest points that correspond to rigid parts. This selection is driven by the spatial relationships and the movement of the interest points. Then, a graph pyramid is built, guided by the orientation changes of the object parts in the scene. This leads to a decomposition of the scene into its rigid parts. Each vertex in the top level of the pyramid represents one rigid part in the scene.
Structural pattern recognition describes and classifies data based on the relationships of featur... more Structural pattern recognition describes and classifies data based on the relationships of features and parts. Topological invariants, like the Euler number, characterize the structure of objects of any dimension. Cohomology can provide more refined algebraic invariants to a topological space than does homology. It assigns ‘quantities’ to the chains used in homology to characterize holes of any dimension. Graph pyramids can be used to describe subdivisions of the same object at multiple levels of detail. This paper presents cohomology in the context of structural pattern recognition and introduces an algorithm to efficiently compute representative cocycles (the basic elements of cohomology) in 2D using a graph pyramid. Extension to nD and application in the context of pattern recognition are discussed.
In this paper we use different decimation strategies in irregular pyramid segmentation framework,... more In this paper we use different decimation strategies in irregular pyramid segmentation framework, to produce perceptually important groupings. These graph decimation strategies, based on the maximum independent set concept, used in Borůvka’s minimum spanning tree based partitioning method, show similar discrepancy segmentation errors. Global and local consistency error measures do not show big differences between the methods although human visual inspection of the results show advantages for one method. To a certain extent this subjective impression is captured by the new criteria of ’region size variation’.
We introduce a method for computing homology groups and their generators of a 2D image, using a h... more We introduce a method for computing homology groups and their generators of a 2D image, using a hierarchical structure i.e. irregular graph pyramid. Starting from an image, a hierarchy of the image is built, by two operations that preserve homology of each region. Instead of computing homology generators in the base where the number of entities (cells) is large, we first reduce the number of cells by a graph pyramid. Then homology generators are computed efficiently on the top level of the pyramid, since the number of cells is small, and a top down process is then used to deduce homology generators in any level of the pyramid, including the base level i.e. the initial image. We show that the new method produces valid homology generators and present some experimental results.
Uploads
Papers by Adrian Ion