A quantum coordinate-entropy formulated in quantum phase space has been recently proposed togethe... more A quantum coordinate-entropy formulated in quantum phase space has been recently proposed together with an entropy law that asserts that such entropy can not decrease over time. The coordinate-entropy is dimensionless, a relativistic scalar, and it is invariant under coordinate and CPT transformations. We study here the time evolution of this entropy. We show that the entropy associated with coherent states evolving under a Dirac Hamiltonian is increasing. However, for the collisions of two particles, where each is evolving as a coherent state, as they come closer to each other their spatial entanglement causes the total system's entropy to oscillate. We augment time reversal with time translation and show that CPT with time translation can transform particles with decreasing entropy for a finite time interval into anti-particles with increasing entropy for the same finite time interval. We then analyze the impact of the entropy law for the evolution scenarios described above and explore the possibility that entropy oscillations trigger the annihilation and the creation of particles.
We describe a statistical approach to the problem of estimating the times of cell-division cycles... more We describe a statistical approach to the problem of estimating the times of cell-division cycles in time-lapse movies of early mouse embryos. Our method is based on the likelihoods for cells of certain radii ranges to be in each frame-without actually locating or counting the cells. Computing the likelihoods consists of a voting scheme where votes come form quadruples of points in a way similar to the first step of the Randomized Hough Transform for ellipse detection. To locate divisions, we search for points of abrupt change in the matrix of likelihoods (built for all frames), and pick the two optimal division points using a dynamic programming algorithm. Our results for the first and second cell division cycles differ less than two frames from the medians of the annotated times in a database of 100 annotated videos, and outperform two other recent methods in the same set.
We introduce a novel and adaptive batch-wise regularization based on the proposed Batch Confusion... more We introduce a novel and adaptive batch-wise regularization based on the proposed Batch Confusion Norm (BCN) to flexibly address the natural world distribution which usually involves fine-grained and long-tailed properties at the same time. The Fine-Grained Visual Classification (FGVC) problem is notably characterized by two intriguing properties, significant inter-class similarity and intra-class variations, which cause learning an effective FGVC classifier a challenging task. Existing techniques attempt to capture the discriminative parts by their modified attention mechanism. The long-tailed distribution of visual classification poses a great challenge for handling the class imbalance problem. Most of existing solutions usually focus on the class-balancing strategies, classifier normalization, or alleviating the negative gradient of tailed categories. Depart from the conventional approaches, we propose to tackle both problems simultaneously with the adaptive confusion concept. When inter-class similarity prevails in a batch, the BCN term can alleviate possible overfitting due to exploring image features of fine details. On the other hand, when inter-class similarity is not an issue, the class predictions from different samples would unavoidably yield a substantial BCN loss, and prompt the network learning to further reduce the cross-entropy loss. More importantly, extending the existing confusion energy-based framework to account for long-tailed scenario, BCN can learn to exert proper distribution of confusion strength over tailed and head categories to improve classification performance. While the resulting FGVC model by the BCN technique is effective, the performance can be consistently boosted by incorporating extra attention mechanism. In our experiments, we have obtained state-of-the-art results on several benchmark FGVC datasets, and also demonstrated that our approach is competitive on the popular natural world distribution dataset, iNaturalist2018.
In this paper we report a database and a series of techniques related to the problem of tracking ... more In this paper we report a database and a series of techniques related to the problem of tracking cells, and detecting their divisions, in time-lapse movies of mammalian embryos. Our contributions are: (1) a method for counting embryos in a well, and cropping each individual embryo across frames, to create individual movies for cell tracking; (2) a semi-automated method for cell tracking that works up to the 8-cell stage, along with a software implementation available to the public (this software was used to build the reported database); (3) an algorithm for automatic tracking up to the 4-cell stage, based on histograms of mirror symmetry coefficients captured using wavelets; (4) a cell-tracking database containing 100 annotated examples of mammalian embryos up to the 8-cell stage; (5) statistical analysis of various timing distributions obtained from those examples.
In human perception, convex surfaces have a strong tendency to be perceived as the "figure". Conv... more In human perception, convex surfaces have a strong tendency to be perceived as the "figure". Convexity has a stronger influence on figural organization than other global shape properties, such as symmetry ([9]). And yet, there has been very little work on convexity properties in computer vision. We present a model for figure/ground segregatation which exhibits a preference for convex regions as the figure (i.e., the foreground). The model also shows a preference for smaller regions to be selected as figures, which is also known to hold for human visual perception (e.g., Koffka [11]). The model is based on the machinery of Markov random fields/random walks/diffusion processes, so that the global shape properties are obtained via local and stochastic computations. Experimental results demonstrate that our model performs well on ambiguous figure/ground displays which were not captured before. In particular, in ambiguous displays where neither region is strictly convex, the model shows preference to the "more convex" region, thus offering a continuous measure of convexity in agreement with human perception.
Quantum physics, despite its observables being intrinsically of a probabilistic nature, does not ... more Quantum physics, despite its observables being intrinsically of a probabilistic nature, does not have a quantum entropy assigned to them. We propose a quantum entropy that quantify the randomness of a pure quantum state via a conjugate pair of observables forming the quantum phase space. The entropy is dimensionless, it is a relativistic scalar, it is invariant under coordinate transformation of position and momentum that maintain conjugate properties, and under CPT transformations; and its minimum is positive due to the uncertainty principle. We expand the entropy to also include mixed states and show that the proposed entropy is always larger than von Neumann's entropy. We conjecture an entropy law whereby that entropy of a closed system never decreases, implying a time arrow for particles physics.
Counting the number of clusters, when these clusters overlap significantly is a challenging probl... more Counting the number of clusters, when these clusters overlap significantly is a challenging problem in machine learning. We argue that a purely mathematical quantum theory, formulated using the path integral technique, when applied to non-physics modeling leads to non-physics quantum theories that are statistical in nature. We show that a quantum theory can be a more robust statistical theory to separate data to count overlapping clusters. The theory is also confirmed from data simulations. This works identify how quantum theory can be effective in counting clusters and hope to inspire the field to further apply such techniques.
It is important in many applications of 3D and higher dimensional segmentation that the resulting... more It is important in many applications of 3D and higher dimensional segmentation that the resulting segments of voxels are not required to have only one connected component, as in some of extant methods. Indeed, it is generally necessary to be able to automatically determine the appropriate number of connected components. More generally, for a larger class of applications, the segments should have no topological restrictions at all. For instance, each connected component should be allowed to have as many holes as appropriate to fit the data. We propose a method based on a graph algorithm to automatically segment 3D and higher-dimensional images into two segments without user intervention, with no topological restriction on the solution, and in such a way that the solution is optimal under a precisely defined optimization criterion.
With the development of deep learning, standard classification problems have achieved good result... more With the development of deep learning, standard classification problems have achieved good results. However, conventional classification problems are often too idealistic. Most data in the natural world usually have imbalanced distribution and fine-grained characteristics. Recently, many state-of-the-art approaches tend to focus on one or another separately, but rarely on both. In this paper, we introduce a novel and adaptive batch-wise regularization based on the proposed Adaptive Confusion Energy (ACE) to flexibly address the nature world distribution, which usually involves fine-grained and long-tailed properties at the same time. ACE increases the difficulty of the training process and further alleviates the overfitting problem. Through the datasets with the technical issue in fine-grained (CUB, CAR, AIR) and long-tailed (ImageNet-LT), or comprehensive issues (CUB-LT, iNaturalist), the result shows that the ACE is not only competitive to some state-ofthe-art on performance but also demonstrates the effectiveness of training.
A quantum coordinate-entropy formulated in quantum phase space has been recently proposed togethe... more A quantum coordinate-entropy formulated in quantum phase space has been recently proposed together with an entropy law that asserts that such entropy can not decrease over time. The coordinate-entropy is dimensionless, a relativistic scalar, and it is invariant under coordinate and CPT transformations. We study here the time evolution of this entropy. We show that the entropy associated with coherent states evolving under a Dirac Hamiltonian is increasing. However, for the collisions of two particles, where each is evolving as a coherent state, as they come closer to each other their spatial entanglement causes the total system's entropy to oscillate. We augment time reversal with time translation and show that CPT with time translation can transform particles with decreasing entropy for a finite time interval into anti-particles with increasing entropy for the same finite time interval. We then analyze the impact of the entropy law for the evolution scenarios described above and explore the possibility that entropy oscillations trigger the annihilation and the creation of particles.
We study particles with spins 1/2 and 1, and define their entropy, a measure of randomness over t... more We study particles with spins 1/2 and 1, and define their entropy, a measure of randomness over the observable spin values given a spin state. Specifying the degrees of freedom of a particle spin state does not provide the knowledge of the spin value in all three dimensional directions. This randomness is formally rooted on the non-commutative properties of the spin operators S_x, S_y, S_z. Our proposed spin-entropy is a measure of the randomness of all three dimensional directions of a spin. This spin-entropy, in contrast to von Neumann entropy, may have non-zero values for pure states. The proposed spin-entropy when applied to Bell states, which are pure entangled states of two fermions, yields local minima values. This suggests that decoherence and disentanglement increases this entropy. The proposed entropy may be useful for the understanding of phenomena that explore the information content of spin systems, including quantum computational processes.
Proceedings of the Seventh IEEE International Conference on Computer Vision, 1999
In human perception, convex surfaces have a strong tendency to be perceived as the "figure". Conv... more In human perception, convex surfaces have a strong tendency to be perceived as the "figure". Convexity has a stronger influence on figural organization than other global shape properties, such as symmetry ([9]). And yet, there has been very little work on convexity properties in computer vision. We present a model for figure/ground segregatation which exhibits a preference for convex regions as the figure (i.e., the foreground). The model also shows a preference for smaller regions to be selected as figures, which is also known to hold for human visual perception (e.g., Koffka [11]). The model is based on the machinery of Markov random fields/random walks/diffusion processes, so that the global shape properties are obtained via local and stochastic computations. Experimental results demonstrate that our model performs well on ambiguous figure/ground displays which were not captured before. In particular, in ambiguous displays where neither region is strictly convex, the model shows preference to the "more convex" region, thus offering a continuous measure of convexity in agreement with human perception.
We introduce a regularization concept based on the proposed Batch Confusion Norm (BCN) to address... more We introduce a regularization concept based on the proposed Batch Confusion Norm (BCN) to address Fine-Grained Visual Classification (FGVC). The FGVC problem is notably characterized by its two intriguing properties, significant inter-class similarity and intra-class variations, which cause learning an effective FGVC classifier a challenging task. Inspired by the use of pairwise confusion energy as a regularization mechanism, we develop the BCN technique to improve the FGVC learning by imposing class prediction confusion on each training batch, and consequently alleviate the possible overfitting due to exploring image feature of fine details. In addition, our method is implemented with an attention gated CNN model, boosted by the incorporation of Atrous Spatial Pyramid Pooling (ASPP) to extract discriminative features and proper attentions. To demonstrate the usefulness of our method, we report state-of-the-art results on several benchmark FGVC datasets, along with comprehensive abl...
We present a convolutional approach to reflection symmetry detection in 2D. Our model, built on t... more We present a convolutional approach to reflection symmetry detection in 2D. Our model, built on the products of complex-valued wavelet convolutions, simplifies previous edgebased pairwise methods. Being parameter-centered, as opposed to feature-centered, it has certain computational advantages when the object sizes are known a priori, as demonstrated in an ellipse detection application. The method outperforms the best-performing algorithm on the CVPR 2013 Symmetry Detection Competition Database in the single-symmetry case. Code and a new database for 2D symmetry detection is available.
An image is often represented by a set of detected features. We get an enormous compression by re... more An image is often represented by a set of detected features. We get an enormous compression by representing images in this way. Furthermore, we get a representation which is little affected by small amounts of noise in the image. However, features are typically chosen in an ad hoc manner. \Ve show how a good set of features can be obtained using sufficient statistics. The idea of sparse data representation naturally arises. We treat the I-dimensional and 2-dimensional signal reconstruction problem to make our ideas concrete.
Proceedings CVPR IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 1996
We are given an image I and a library of templates L, such that L is an overcomplete basis for I.... more We are given an image I and a library of templates L, such that L is an overcomplete basis for I. The templates can represent objects, faces, features, analytical functions, or be single pixel templates (canonical templates). There are infinitely many ways to decompose I as a linear combination of the library templates. Each decomposition defines a representation for the image I, given L. What is an optimal representation for I given L and how to select it? We are motivated to select a sparse/compact representation for I, and to account for occlusions and noise in the image. We present a concave cost function criterion on the linear decomposition coefficients that satisfies our requirements. More specifically, we study a "weighted L p norm" with 0 < p < 1. We prove a result that allows us to generate all local minima for the L p norm, and the global minimum is obtained by searching through the local ones. Due to the computational complexity, i.e., the large number of local minima, we also study a greedy and iterative "weighted L p Matching Pursuit" strategy.
2014 IEEE International Conference on Image Processing (ICIP), 2014
We describe a statistical approach to the problem of estimating the times of cell-division cycles... more We describe a statistical approach to the problem of estimating the times of cell-division cycles in time-lapse movies of early mouse embryos. Our method is based on the likelihoods for cells of certain radii ranges to be in each frame-without actually locating or counting the cells. Computing the likelihoods consists of a voting scheme where votes come form quadruples of points in a way similar to the first step of the Randomized Hough Transform for ellipse detection. To locate divisions, we search for points of abrupt change in the matrix of likelihoods (built for all frames), and pick the two optimal division points using a dynamic programming algorithm. Our results for the first and second cell division cycles differ less than two frames from the medians of the annotated times in a database of 100 annotated videos, and outperform two other recent methods in the same set.
Tenth IEEE International Conference on Computer Vision (ICCV'05) Volume 1, 2005
The representation of objects in images as tree structures is of great interest to vision, as the... more The representation of objects in images as tree structures is of great interest to vision, as they can represent articulated objects such as people as well as other structured objects like arteries in human bodies, roads, circuit board patterns, etc. Tree structures are often related to the symmetry axis representation of shapes, which captures their local symmetries. Algorithms have been introduced to detect (i) open contours in images in quadratic time (ii) closed contours in images in cubic time, and (iii) tree structures from contours in quadratic time. The algorithms are based on dynamic programming and Single Source Shortest Path algorithms. However, in this paper, we show that the problem of finding tree structures in images in a principled manner is a much harder problem. We argue that the optimization problem of finding tree structures in images is essentially equivalent to a variant of the Steiner Tree problem, which is NP-hard. Nevertheless, an approximate polynomial-time algorithm for this problem exists: we apply a fast implementation of the Goemans-Williamson approximate algorithm to the problem of finding a tree representation after an image is transformed by a local symmetry mapping. Examples of extracting tree structures from images illustrate the idea and applicability of the approximate method.
It is important in many applications of 3D and higher dimensional segmentation that the resulting... more It is important in many applications of 3D and higher dimensional segmentation that the resulting segments of voxels are not required to have only one connected component, as in some of extant methods. Indeed, it is generally necessary to be able to automatically determine the appropriate number of connected components. More generally, for a larger class of applications, the segments should have no topological restrictions at all. For instance, each connected component should be allowed to have as many holes as appropriate to fit the data. We propose a method based on a graph algorithm to automatically segment 3D and higher-dimensional images into two segments without user intervention, with no topological restriction on the solution, and in such a way that the solution is optimal under a precisely defined optimization criterion.
2014 IEEE International Conference on Image Processing (ICIP), 2014
We present an ellipse finding and fitting algorithm that uses points and tangents, rather than ju... more We present an ellipse finding and fitting algorithm that uses points and tangents, rather than just points, as the basic unit of information. These units are analyzed in a hierarchy: points with tangents are paired into triangles in the first layer and pairs of triangles in the second layer vote for ellipse centers. The remaining parameters are estimated via robust linear algebra: eigen-decomposition and iteratively reweighed least squares. Our method outperforms the state-of-the-art approach in synthetic images and microscopic images of cells.
A quantum coordinate-entropy formulated in quantum phase space has been recently proposed togethe... more A quantum coordinate-entropy formulated in quantum phase space has been recently proposed together with an entropy law that asserts that such entropy can not decrease over time. The coordinate-entropy is dimensionless, a relativistic scalar, and it is invariant under coordinate and CPT transformations. We study here the time evolution of this entropy. We show that the entropy associated with coherent states evolving under a Dirac Hamiltonian is increasing. However, for the collisions of two particles, where each is evolving as a coherent state, as they come closer to each other their spatial entanglement causes the total system's entropy to oscillate. We augment time reversal with time translation and show that CPT with time translation can transform particles with decreasing entropy for a finite time interval into anti-particles with increasing entropy for the same finite time interval. We then analyze the impact of the entropy law for the evolution scenarios described above and explore the possibility that entropy oscillations trigger the annihilation and the creation of particles.
We describe a statistical approach to the problem of estimating the times of cell-division cycles... more We describe a statistical approach to the problem of estimating the times of cell-division cycles in time-lapse movies of early mouse embryos. Our method is based on the likelihoods for cells of certain radii ranges to be in each frame-without actually locating or counting the cells. Computing the likelihoods consists of a voting scheme where votes come form quadruples of points in a way similar to the first step of the Randomized Hough Transform for ellipse detection. To locate divisions, we search for points of abrupt change in the matrix of likelihoods (built for all frames), and pick the two optimal division points using a dynamic programming algorithm. Our results for the first and second cell division cycles differ less than two frames from the medians of the annotated times in a database of 100 annotated videos, and outperform two other recent methods in the same set.
We introduce a novel and adaptive batch-wise regularization based on the proposed Batch Confusion... more We introduce a novel and adaptive batch-wise regularization based on the proposed Batch Confusion Norm (BCN) to flexibly address the natural world distribution which usually involves fine-grained and long-tailed properties at the same time. The Fine-Grained Visual Classification (FGVC) problem is notably characterized by two intriguing properties, significant inter-class similarity and intra-class variations, which cause learning an effective FGVC classifier a challenging task. Existing techniques attempt to capture the discriminative parts by their modified attention mechanism. The long-tailed distribution of visual classification poses a great challenge for handling the class imbalance problem. Most of existing solutions usually focus on the class-balancing strategies, classifier normalization, or alleviating the negative gradient of tailed categories. Depart from the conventional approaches, we propose to tackle both problems simultaneously with the adaptive confusion concept. When inter-class similarity prevails in a batch, the BCN term can alleviate possible overfitting due to exploring image features of fine details. On the other hand, when inter-class similarity is not an issue, the class predictions from different samples would unavoidably yield a substantial BCN loss, and prompt the network learning to further reduce the cross-entropy loss. More importantly, extending the existing confusion energy-based framework to account for long-tailed scenario, BCN can learn to exert proper distribution of confusion strength over tailed and head categories to improve classification performance. While the resulting FGVC model by the BCN technique is effective, the performance can be consistently boosted by incorporating extra attention mechanism. In our experiments, we have obtained state-of-the-art results on several benchmark FGVC datasets, and also demonstrated that our approach is competitive on the popular natural world distribution dataset, iNaturalist2018.
In this paper we report a database and a series of techniques related to the problem of tracking ... more In this paper we report a database and a series of techniques related to the problem of tracking cells, and detecting their divisions, in time-lapse movies of mammalian embryos. Our contributions are: (1) a method for counting embryos in a well, and cropping each individual embryo across frames, to create individual movies for cell tracking; (2) a semi-automated method for cell tracking that works up to the 8-cell stage, along with a software implementation available to the public (this software was used to build the reported database); (3) an algorithm for automatic tracking up to the 4-cell stage, based on histograms of mirror symmetry coefficients captured using wavelets; (4) a cell-tracking database containing 100 annotated examples of mammalian embryos up to the 8-cell stage; (5) statistical analysis of various timing distributions obtained from those examples.
In human perception, convex surfaces have a strong tendency to be perceived as the "figure". Conv... more In human perception, convex surfaces have a strong tendency to be perceived as the "figure". Convexity has a stronger influence on figural organization than other global shape properties, such as symmetry ([9]). And yet, there has been very little work on convexity properties in computer vision. We present a model for figure/ground segregatation which exhibits a preference for convex regions as the figure (i.e., the foreground). The model also shows a preference for smaller regions to be selected as figures, which is also known to hold for human visual perception (e.g., Koffka [11]). The model is based on the machinery of Markov random fields/random walks/diffusion processes, so that the global shape properties are obtained via local and stochastic computations. Experimental results demonstrate that our model performs well on ambiguous figure/ground displays which were not captured before. In particular, in ambiguous displays where neither region is strictly convex, the model shows preference to the "more convex" region, thus offering a continuous measure of convexity in agreement with human perception.
Quantum physics, despite its observables being intrinsically of a probabilistic nature, does not ... more Quantum physics, despite its observables being intrinsically of a probabilistic nature, does not have a quantum entropy assigned to them. We propose a quantum entropy that quantify the randomness of a pure quantum state via a conjugate pair of observables forming the quantum phase space. The entropy is dimensionless, it is a relativistic scalar, it is invariant under coordinate transformation of position and momentum that maintain conjugate properties, and under CPT transformations; and its minimum is positive due to the uncertainty principle. We expand the entropy to also include mixed states and show that the proposed entropy is always larger than von Neumann's entropy. We conjecture an entropy law whereby that entropy of a closed system never decreases, implying a time arrow for particles physics.
Counting the number of clusters, when these clusters overlap significantly is a challenging probl... more Counting the number of clusters, when these clusters overlap significantly is a challenging problem in machine learning. We argue that a purely mathematical quantum theory, formulated using the path integral technique, when applied to non-physics modeling leads to non-physics quantum theories that are statistical in nature. We show that a quantum theory can be a more robust statistical theory to separate data to count overlapping clusters. The theory is also confirmed from data simulations. This works identify how quantum theory can be effective in counting clusters and hope to inspire the field to further apply such techniques.
It is important in many applications of 3D and higher dimensional segmentation that the resulting... more It is important in many applications of 3D and higher dimensional segmentation that the resulting segments of voxels are not required to have only one connected component, as in some of extant methods. Indeed, it is generally necessary to be able to automatically determine the appropriate number of connected components. More generally, for a larger class of applications, the segments should have no topological restrictions at all. For instance, each connected component should be allowed to have as many holes as appropriate to fit the data. We propose a method based on a graph algorithm to automatically segment 3D and higher-dimensional images into two segments without user intervention, with no topological restriction on the solution, and in such a way that the solution is optimal under a precisely defined optimization criterion.
With the development of deep learning, standard classification problems have achieved good result... more With the development of deep learning, standard classification problems have achieved good results. However, conventional classification problems are often too idealistic. Most data in the natural world usually have imbalanced distribution and fine-grained characteristics. Recently, many state-of-the-art approaches tend to focus on one or another separately, but rarely on both. In this paper, we introduce a novel and adaptive batch-wise regularization based on the proposed Adaptive Confusion Energy (ACE) to flexibly address the nature world distribution, which usually involves fine-grained and long-tailed properties at the same time. ACE increases the difficulty of the training process and further alleviates the overfitting problem. Through the datasets with the technical issue in fine-grained (CUB, CAR, AIR) and long-tailed (ImageNet-LT), or comprehensive issues (CUB-LT, iNaturalist), the result shows that the ACE is not only competitive to some state-ofthe-art on performance but also demonstrates the effectiveness of training.
A quantum coordinate-entropy formulated in quantum phase space has been recently proposed togethe... more A quantum coordinate-entropy formulated in quantum phase space has been recently proposed together with an entropy law that asserts that such entropy can not decrease over time. The coordinate-entropy is dimensionless, a relativistic scalar, and it is invariant under coordinate and CPT transformations. We study here the time evolution of this entropy. We show that the entropy associated with coherent states evolving under a Dirac Hamiltonian is increasing. However, for the collisions of two particles, where each is evolving as a coherent state, as they come closer to each other their spatial entanglement causes the total system's entropy to oscillate. We augment time reversal with time translation and show that CPT with time translation can transform particles with decreasing entropy for a finite time interval into anti-particles with increasing entropy for the same finite time interval. We then analyze the impact of the entropy law for the evolution scenarios described above and explore the possibility that entropy oscillations trigger the annihilation and the creation of particles.
We study particles with spins 1/2 and 1, and define their entropy, a measure of randomness over t... more We study particles with spins 1/2 and 1, and define their entropy, a measure of randomness over the observable spin values given a spin state. Specifying the degrees of freedom of a particle spin state does not provide the knowledge of the spin value in all three dimensional directions. This randomness is formally rooted on the non-commutative properties of the spin operators S_x, S_y, S_z. Our proposed spin-entropy is a measure of the randomness of all three dimensional directions of a spin. This spin-entropy, in contrast to von Neumann entropy, may have non-zero values for pure states. The proposed spin-entropy when applied to Bell states, which are pure entangled states of two fermions, yields local minima values. This suggests that decoherence and disentanglement increases this entropy. The proposed entropy may be useful for the understanding of phenomena that explore the information content of spin systems, including quantum computational processes.
Proceedings of the Seventh IEEE International Conference on Computer Vision, 1999
In human perception, convex surfaces have a strong tendency to be perceived as the "figure". Conv... more In human perception, convex surfaces have a strong tendency to be perceived as the "figure". Convexity has a stronger influence on figural organization than other global shape properties, such as symmetry ([9]). And yet, there has been very little work on convexity properties in computer vision. We present a model for figure/ground segregatation which exhibits a preference for convex regions as the figure (i.e., the foreground). The model also shows a preference for smaller regions to be selected as figures, which is also known to hold for human visual perception (e.g., Koffka [11]). The model is based on the machinery of Markov random fields/random walks/diffusion processes, so that the global shape properties are obtained via local and stochastic computations. Experimental results demonstrate that our model performs well on ambiguous figure/ground displays which were not captured before. In particular, in ambiguous displays where neither region is strictly convex, the model shows preference to the "more convex" region, thus offering a continuous measure of convexity in agreement with human perception.
We introduce a regularization concept based on the proposed Batch Confusion Norm (BCN) to address... more We introduce a regularization concept based on the proposed Batch Confusion Norm (BCN) to address Fine-Grained Visual Classification (FGVC). The FGVC problem is notably characterized by its two intriguing properties, significant inter-class similarity and intra-class variations, which cause learning an effective FGVC classifier a challenging task. Inspired by the use of pairwise confusion energy as a regularization mechanism, we develop the BCN technique to improve the FGVC learning by imposing class prediction confusion on each training batch, and consequently alleviate the possible overfitting due to exploring image feature of fine details. In addition, our method is implemented with an attention gated CNN model, boosted by the incorporation of Atrous Spatial Pyramid Pooling (ASPP) to extract discriminative features and proper attentions. To demonstrate the usefulness of our method, we report state-of-the-art results on several benchmark FGVC datasets, along with comprehensive abl...
We present a convolutional approach to reflection symmetry detection in 2D. Our model, built on t... more We present a convolutional approach to reflection symmetry detection in 2D. Our model, built on the products of complex-valued wavelet convolutions, simplifies previous edgebased pairwise methods. Being parameter-centered, as opposed to feature-centered, it has certain computational advantages when the object sizes are known a priori, as demonstrated in an ellipse detection application. The method outperforms the best-performing algorithm on the CVPR 2013 Symmetry Detection Competition Database in the single-symmetry case. Code and a new database for 2D symmetry detection is available.
An image is often represented by a set of detected features. We get an enormous compression by re... more An image is often represented by a set of detected features. We get an enormous compression by representing images in this way. Furthermore, we get a representation which is little affected by small amounts of noise in the image. However, features are typically chosen in an ad hoc manner. \Ve show how a good set of features can be obtained using sufficient statistics. The idea of sparse data representation naturally arises. We treat the I-dimensional and 2-dimensional signal reconstruction problem to make our ideas concrete.
Proceedings CVPR IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 1996
We are given an image I and a library of templates L, such that L is an overcomplete basis for I.... more We are given an image I and a library of templates L, such that L is an overcomplete basis for I. The templates can represent objects, faces, features, analytical functions, or be single pixel templates (canonical templates). There are infinitely many ways to decompose I as a linear combination of the library templates. Each decomposition defines a representation for the image I, given L. What is an optimal representation for I given L and how to select it? We are motivated to select a sparse/compact representation for I, and to account for occlusions and noise in the image. We present a concave cost function criterion on the linear decomposition coefficients that satisfies our requirements. More specifically, we study a "weighted L p norm" with 0 < p < 1. We prove a result that allows us to generate all local minima for the L p norm, and the global minimum is obtained by searching through the local ones. Due to the computational complexity, i.e., the large number of local minima, we also study a greedy and iterative "weighted L p Matching Pursuit" strategy.
2014 IEEE International Conference on Image Processing (ICIP), 2014
We describe a statistical approach to the problem of estimating the times of cell-division cycles... more We describe a statistical approach to the problem of estimating the times of cell-division cycles in time-lapse movies of early mouse embryos. Our method is based on the likelihoods for cells of certain radii ranges to be in each frame-without actually locating or counting the cells. Computing the likelihoods consists of a voting scheme where votes come form quadruples of points in a way similar to the first step of the Randomized Hough Transform for ellipse detection. To locate divisions, we search for points of abrupt change in the matrix of likelihoods (built for all frames), and pick the two optimal division points using a dynamic programming algorithm. Our results for the first and second cell division cycles differ less than two frames from the medians of the annotated times in a database of 100 annotated videos, and outperform two other recent methods in the same set.
Tenth IEEE International Conference on Computer Vision (ICCV'05) Volume 1, 2005
The representation of objects in images as tree structures is of great interest to vision, as the... more The representation of objects in images as tree structures is of great interest to vision, as they can represent articulated objects such as people as well as other structured objects like arteries in human bodies, roads, circuit board patterns, etc. Tree structures are often related to the symmetry axis representation of shapes, which captures their local symmetries. Algorithms have been introduced to detect (i) open contours in images in quadratic time (ii) closed contours in images in cubic time, and (iii) tree structures from contours in quadratic time. The algorithms are based on dynamic programming and Single Source Shortest Path algorithms. However, in this paper, we show that the problem of finding tree structures in images in a principled manner is a much harder problem. We argue that the optimization problem of finding tree structures in images is essentially equivalent to a variant of the Steiner Tree problem, which is NP-hard. Nevertheless, an approximate polynomial-time algorithm for this problem exists: we apply a fast implementation of the Goemans-Williamson approximate algorithm to the problem of finding a tree representation after an image is transformed by a local symmetry mapping. Examples of extracting tree structures from images illustrate the idea and applicability of the approximate method.
It is important in many applications of 3D and higher dimensional segmentation that the resulting... more It is important in many applications of 3D and higher dimensional segmentation that the resulting segments of voxels are not required to have only one connected component, as in some of extant methods. Indeed, it is generally necessary to be able to automatically determine the appropriate number of connected components. More generally, for a larger class of applications, the segments should have no topological restrictions at all. For instance, each connected component should be allowed to have as many holes as appropriate to fit the data. We propose a method based on a graph algorithm to automatically segment 3D and higher-dimensional images into two segments without user intervention, with no topological restriction on the solution, and in such a way that the solution is optimal under a precisely defined optimization criterion.
2014 IEEE International Conference on Image Processing (ICIP), 2014
We present an ellipse finding and fitting algorithm that uses points and tangents, rather than ju... more We present an ellipse finding and fitting algorithm that uses points and tangents, rather than just points, as the basic unit of information. These units are analyzed in a hierarchy: points with tangents are paired into triangles in the first layer and pairs of triangles in the second layer vote for ellipse centers. The remaining parameters are estimated via robust linear algebra: eigen-decomposition and iteratively reweighed least squares. Our method outperforms the state-of-the-art approach in synthetic images and microscopic images of cells.
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Papers by Davi Geiger