The Experts below are selected from a list of 189 Experts worldwide ranked by ideXlab platform
Frank H. Lutz - One of the best experts on this subject based on the ideXlab platform.
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Extremal Examples of Collapsible Complexes and Random Discrete Morse Theory
Discrete & Computational Geometry, 2017Co-Authors: Karim Adiprasito, Bruno Benedetti, Frank H. LutzAbstract:We present extremal constructions connected with the property of simplicial collapsibility. (1) For each $$d \ge 2$$ d ≥ 2 , there are collapsible (and shellable) simplicial d -complexes with only one free Face. Also, there are non-evasive d -complexes with only two free Faces (both results are optimal in all dimensions). (2) Optimal discrete Morse Vectors need not be unique. We explicitly construct a contractible, but non-collapsible 3-dimensional simplicial complex with Face Vector $$f=(106,596,1064,573)$$ f = ( 106 , 596 , 1064 , 573 ) that admits two distinct optimal discrete Morse Vectors, (1, 1, 1, 0) and (1, 0, 1, 1). Indeed, we show that in every dimension $$d\ge 3$$ d ≥ 3 there are contractible, non-collapsible simplicial d -complexes that have $$(1,0,\dots ,0,1,1,0)$$ ( 1 , 0 , ⋯ , 0 , 1 , 1 , 0 ) and $$(1,0,\dots ,0,0,1,1)$$ ( 1 , 0 , ⋯ , 0 , 0 , 1 , 1 ) as distinct optimal discrete Morse Vectors. (3) We give a first explicit example of a (non-PL) 5-manifold, with Face Vector $$f=(5013,72300,290944,$$ f = ( 5013 , 72300 , 290944 , 495912, 383136, 110880), that is collapsible but not homeomorphic to a ball. Furthermore, we discuss possible improvements and drawbacks of random approaches to collapsibility and discrete Morse theory. We will introduce randomized versions random-lex-first and random-lex-last of the lex-first and lex-last discrete Morse strategies of Benedetti and Lutz (Exp Math 23(1):66–94, 2014 ), respectively—and we will see that in many instances the random-lex-last strategy works significantly better than Benedetti–Lutz’s (uniform) random strategy. On the theoretical side, we prove that after repeated barycentric subdivisions, the discrete Morse Vectors found by randomized algorithms have, on average, an exponential (in the number of barycentric subdivisions) number of critical cells asymptotically almost surely.
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Chromatic Numbers of Simplicial Manifolds
arXiv: Combinatorics, 2015Co-Authors: Frank H. Lutz, Jesper M. MøllerAbstract:Higher chromatic numbers of simplicial complexes naturally generalize the chromatic number of a graph. Yet, little is known on higher chromatic numbers for specific simplicial complexes. The 2-chromatic number of any fixed surFace is finite. However, asymptotically the 2-chromatic number of surFaces becomes arbitrarily large with growing genus (as we will see via Steiner triple systems). We show that orientable surFaces of genus at least 20 and non-orientable surFaces of genus at least 26 have a 2-chromatic number of at least 4. Via a projective Steiner triple systems, we construct an explicit triangulation of a non-orientable surFace, of genus 2542 and with Face Vector $f=(127,8001,5334)$, that has 2-chromatic number 5 or 6. We also give orientable examples with 2-chromatic numbers 5 and 6. For 3-dimensional manifolds, an iterated moment curve construction can be used to produce triangulations with arbitrarily large 2-chromatic number [6, 18], but of tremendous size. Via a topological version of the geometric construction of [18], we exhibit the first concrete triangulation of the 3-dimension sphere $S^3$, with Face Vector $f=(167,1579,2824,1412)$, that has 2-chromatic number 5.
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Extremal examples of collapsible complexes and random discrete Morse theory
arXiv: Combinatorics, 2014Co-Authors: Karim Adiprasito, Bruno Benedetti, Frank H. LutzAbstract:We present extremal constructions connected with the property of simplicial collapsibility. (1) For each $d \ge 2$, there are collapsible (and shellable) simplicial $d$-complexes with only one free Face. Also, there are non-evasive $d$-complexes with only two free Faces. (Both results are optimal in all dimensions.) (2) Optimal discrete Morse Vectors need not be unique. We explicitly construct a contractible, but non-collapsible $3$-dimensional simplicial complex with Face Vector $f=(106,596,1064,573)$ that admits two distinct optimal discrete Morse Vectors, $(1,1,1,0)$ and $(1,0,1,1)$. Indeed, we show that in every dimension $d\geq 3$ there are contractible, non-collapsible simplicial $d$-complexes that have $(1,0,\dots,0,1,1,0)$ and $(1,0,\dots,0,0,1,1)$ as distinct optimal discrete Morse Vectors. (3) We give a first explicit example of a (non-PL) $5$-manifold, with Face Vector $f=(5013,72300,290944,$ $495912,383136,110880)$, that is collapsible but not homeomorphic to a ball. Furthermore, we discuss possible improvements and drawbacks of random approaches to collapsibility and discrete Morse theory. We will introduce randomized versions \texttt{random-lex-first} and \texttt{random-lex-last} of the \texttt{lex-first} and \texttt{lex-last} discrete Morse strategies of \cite{BenedettiLutz2014}, respectively --- and we will see that in many instances the \texttt{random-lex-last} strategy works significantly better than Benedetti--Lutz's (uniform) \texttt{random} strategy. On the theoretical side, we prove that after repeated barycentric subdivisions, the discrete Morse Vectors found by randomized algorithms have, on average, an exponential (in the number of barycentric subdivisions) number of critical cells asymptotically almost surely.
Jamuna Kanta Sing - One of the best experts on this subject based on the ideXlab platform.
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Robust Multi-Camera View Face Recognition
International Journal of Computers and Applications, 2020Co-Authors: Dakshina Ranjan Kisku, Hunny Mehrotra, Phalguni Gupta, Jamuna Kanta SingAbstract:AbstractThis paper presents multi-appearance fusion of principal component analysis (PCA) and generalization of linear discriminant analysis (LDA) for multi-camera view offline Face recognition (verification) system. The generalization of LDA has been extended to establish correlations between the Face classes in the transformed representation and this is called canonical covariate. The proposed system uses Gabor filter banks for characterization of facial features by spatial frequency, spatial locality and orientation to compensate to the variations of Face instances occurred due to illumination, pose and facial expression changes. Convolution of Gabor filter bank to Face images produces Gabor Face representations with high-dimensional feature Vectors. PC A and canonical covariate are then applied on the Gabor Face representations to reduce the high-dimensional feature spaces into low-dimensional Gabor eigenFaces and Gabor canonical Faces. Reduced eigenFace Vector and canonical Face Vector are fused toge...
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Robust multi-camera view Face recognition
arXiv: Computer Vision and Pattern Recognition, 2010Co-Authors: Dakshina Ranjan Kisku, Hunny Mehrotra, Phalguni Gupta, Jamuna Kanta SingAbstract:This paper presents multi-appearance fusion of Principal Component Analysis (PCA) and generalization of Linear Discriminant Analysis (LDA) for multi-camera view offline Face recognition (verification) system. The generalization of LDA has been extended to establish correlations between the Face classes in the transformed representation and this is called canonical covariate. The proposed system uses Gabor filter banks for characterization of facial features by spatial frequency, spatial locality and orientation to make compensate to the variations of Face instances occurred due to illumination, pose and facial expression changes. Convolution of Gabor filter bank to Face images produces Gabor Face representations with high dimensional feature Vectors. PCA and canonical covariate are then applied on the Gabor Face representations to reduce the high dimensional feature spaces into low dimensional Gabor eigenFaces and Gabor canonical Faces. Reduced eigenFace Vector and canonical Face Vector are fused together using weighted mean fusion rule. Finally, support Vector machines (SVM) have trained with augmented fused set of features and perform the recognition task. The system has been evaluated with UMIST Face database consisting of multiview Faces. The experimental results demonstrate the efficiency and robustness of the proposed system for multi-view Face images with high recognition rates. Complexity analysis of the proposed system is also presented at the end of the experimental results.
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Multiview Gabor Face recognition by fusion of PCA and canonical covariate through feature weighting
Proceedings of SPIE, 2009Co-Authors: Dakshina Ranjan Kisku, Hunny Mehrotra, Jamuna Kanta Sing, Ajita Rattani, Phalguni GuptaAbstract:In this paper, fusion of Principal Component Analysis (PCA) and generalization of Linear Discriminant Analysis (LDA) in the context of multiview Face recognition is proposed. The generalization of LDA is extended to establish correlation between Face classes in the transformed representation, which is called canonical covariate. The proposed work uses Gabor filter bank for extracting facial features characterized by spatial frequency, spatial locality and orientation to compensate the variations in Face that occur due to change in illumination, pose and facial expression. Convolution of Gabor filter bank with Face images produces Gabor Face representations with high dimensional feature Vectors. PCA and canonical covariate are then applied on the Gabor Face representations to reduce the high dimensional feature spaces into low dimensional Gabor eigenFaces and Gabor canonical Faces. Reduced eigenFace Vector and canonical Face Vector are fused together using weighted mean fusion rule. Finally, support Vector machines have been trained with augmented fused set of features to perform recognition task. The proposed system has been evaluated with UMIST Face database and performs with higher recognition accuracy for multi-view Face images.
Dakshina Ranjan Kisku - One of the best experts on this subject based on the ideXlab platform.
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Robust Multi-Camera View Face Recognition
International Journal of Computers and Applications, 2020Co-Authors: Dakshina Ranjan Kisku, Hunny Mehrotra, Phalguni Gupta, Jamuna Kanta SingAbstract:AbstractThis paper presents multi-appearance fusion of principal component analysis (PCA) and generalization of linear discriminant analysis (LDA) for multi-camera view offline Face recognition (verification) system. The generalization of LDA has been extended to establish correlations between the Face classes in the transformed representation and this is called canonical covariate. The proposed system uses Gabor filter banks for characterization of facial features by spatial frequency, spatial locality and orientation to compensate to the variations of Face instances occurred due to illumination, pose and facial expression changes. Convolution of Gabor filter bank to Face images produces Gabor Face representations with high-dimensional feature Vectors. PC A and canonical covariate are then applied on the Gabor Face representations to reduce the high-dimensional feature spaces into low-dimensional Gabor eigenFaces and Gabor canonical Faces. Reduced eigenFace Vector and canonical Face Vector are fused toge...
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Robust multi-camera view Face recognition
arXiv: Computer Vision and Pattern Recognition, 2010Co-Authors: Dakshina Ranjan Kisku, Hunny Mehrotra, Phalguni Gupta, Jamuna Kanta SingAbstract:This paper presents multi-appearance fusion of Principal Component Analysis (PCA) and generalization of Linear Discriminant Analysis (LDA) for multi-camera view offline Face recognition (verification) system. The generalization of LDA has been extended to establish correlations between the Face classes in the transformed representation and this is called canonical covariate. The proposed system uses Gabor filter banks for characterization of facial features by spatial frequency, spatial locality and orientation to make compensate to the variations of Face instances occurred due to illumination, pose and facial expression changes. Convolution of Gabor filter bank to Face images produces Gabor Face representations with high dimensional feature Vectors. PCA and canonical covariate are then applied on the Gabor Face representations to reduce the high dimensional feature spaces into low dimensional Gabor eigenFaces and Gabor canonical Faces. Reduced eigenFace Vector and canonical Face Vector are fused together using weighted mean fusion rule. Finally, support Vector machines (SVM) have trained with augmented fused set of features and perform the recognition task. The system has been evaluated with UMIST Face database consisting of multiview Faces. The experimental results demonstrate the efficiency and robustness of the proposed system for multi-view Face images with high recognition rates. Complexity analysis of the proposed system is also presented at the end of the experimental results.
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Multiview Gabor Face recognition by fusion of PCA and canonical covariate through feature weighting
Proceedings of SPIE, 2009Co-Authors: Dakshina Ranjan Kisku, Hunny Mehrotra, Jamuna Kanta Sing, Ajita Rattani, Phalguni GuptaAbstract:In this paper, fusion of Principal Component Analysis (PCA) and generalization of Linear Discriminant Analysis (LDA) in the context of multiview Face recognition is proposed. The generalization of LDA is extended to establish correlation between Face classes in the transformed representation, which is called canonical covariate. The proposed work uses Gabor filter bank for extracting facial features characterized by spatial frequency, spatial locality and orientation to compensate the variations in Face that occur due to change in illumination, pose and facial expression. Convolution of Gabor filter bank with Face images produces Gabor Face representations with high dimensional feature Vectors. PCA and canonical covariate are then applied on the Gabor Face representations to reduce the high dimensional feature spaces into low dimensional Gabor eigenFaces and Gabor canonical Faces. Reduced eigenFace Vector and canonical Face Vector are fused together using weighted mean fusion rule. Finally, support Vector machines have been trained with augmented fused set of features to perform recognition task. The proposed system has been evaluated with UMIST Face database and performs with higher recognition accuracy for multi-view Face images.
Phalguni Gupta - One of the best experts on this subject based on the ideXlab platform.
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Robust Multi-Camera View Face Recognition
International Journal of Computers and Applications, 2020Co-Authors: Dakshina Ranjan Kisku, Hunny Mehrotra, Phalguni Gupta, Jamuna Kanta SingAbstract:AbstractThis paper presents multi-appearance fusion of principal component analysis (PCA) and generalization of linear discriminant analysis (LDA) for multi-camera view offline Face recognition (verification) system. The generalization of LDA has been extended to establish correlations between the Face classes in the transformed representation and this is called canonical covariate. The proposed system uses Gabor filter banks for characterization of facial features by spatial frequency, spatial locality and orientation to compensate to the variations of Face instances occurred due to illumination, pose and facial expression changes. Convolution of Gabor filter bank to Face images produces Gabor Face representations with high-dimensional feature Vectors. PC A and canonical covariate are then applied on the Gabor Face representations to reduce the high-dimensional feature spaces into low-dimensional Gabor eigenFaces and Gabor canonical Faces. Reduced eigenFace Vector and canonical Face Vector are fused toge...
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Robust multi-camera view Face recognition
arXiv: Computer Vision and Pattern Recognition, 2010Co-Authors: Dakshina Ranjan Kisku, Hunny Mehrotra, Phalguni Gupta, Jamuna Kanta SingAbstract:This paper presents multi-appearance fusion of Principal Component Analysis (PCA) and generalization of Linear Discriminant Analysis (LDA) for multi-camera view offline Face recognition (verification) system. The generalization of LDA has been extended to establish correlations between the Face classes in the transformed representation and this is called canonical covariate. The proposed system uses Gabor filter banks for characterization of facial features by spatial frequency, spatial locality and orientation to make compensate to the variations of Face instances occurred due to illumination, pose and facial expression changes. Convolution of Gabor filter bank to Face images produces Gabor Face representations with high dimensional feature Vectors. PCA and canonical covariate are then applied on the Gabor Face representations to reduce the high dimensional feature spaces into low dimensional Gabor eigenFaces and Gabor canonical Faces. Reduced eigenFace Vector and canonical Face Vector are fused together using weighted mean fusion rule. Finally, support Vector machines (SVM) have trained with augmented fused set of features and perform the recognition task. The system has been evaluated with UMIST Face database consisting of multiview Faces. The experimental results demonstrate the efficiency and robustness of the proposed system for multi-view Face images with high recognition rates. Complexity analysis of the proposed system is also presented at the end of the experimental results.
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Multiview Gabor Face recognition by fusion of PCA and canonical covariate through feature weighting
Proceedings of SPIE, 2009Co-Authors: Dakshina Ranjan Kisku, Hunny Mehrotra, Jamuna Kanta Sing, Ajita Rattani, Phalguni GuptaAbstract:In this paper, fusion of Principal Component Analysis (PCA) and generalization of Linear Discriminant Analysis (LDA) in the context of multiview Face recognition is proposed. The generalization of LDA is extended to establish correlation between Face classes in the transformed representation, which is called canonical covariate. The proposed work uses Gabor filter bank for extracting facial features characterized by spatial frequency, spatial locality and orientation to compensate the variations in Face that occur due to change in illumination, pose and facial expression. Convolution of Gabor filter bank with Face images produces Gabor Face representations with high dimensional feature Vectors. PCA and canonical covariate are then applied on the Gabor Face representations to reduce the high dimensional feature spaces into low dimensional Gabor eigenFaces and Gabor canonical Faces. Reduced eigenFace Vector and canonical Face Vector are fused together using weighted mean fusion rule. Finally, support Vector machines have been trained with augmented fused set of features to perform recognition task. The proposed system has been evaluated with UMIST Face database and performs with higher recognition accuracy for multi-view Face images.
Michael Ingleby - One of the best experts on this subject based on the ideXlab platform.
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Toward Use of Facial Thermal Features in Dynamic Assessment of Affect and Arousal Level
IEEE Transactions on Affective Computing, 2017Co-Authors: Masood Mehmood Khan, Robert D. Ward, Michael InglebyAbstract:Automated assessment of affect and arousal level can help psychologists and psychiatrists in clinical diagnoses; and may enable affect-aware robot-human interaction. This work identifies major difficulties in automating affect and arousal assessment and attempts to overcome some of them. We first analyze thermal infrared images and examine how changes in affect and/or arousal level would cause haemodynamic variations, concentrated along certain facial muscles. These concentrations are used to measure affect/arousal induced facial thermal variations. In step-1 of a 2-step pattern recognition schema, ‘between-affect’ and ‘between-arousal-level’ variations are used to derive facial thermal features as Principal Components (PCs) of the facial thermal measurements. The most influential of these PCs are used to cluster the feature space for different affects and subsequently assign a set of thermal features to an affect cluster. In step-2, affect clusters are partitioned into high, medium and mild arousal levels. The distance between a test Face Vector and the centroids of sub-clusters at three arousal levels belonging to a single affective state, identified from step-1, is used to determine the arousal level of the identified affective state.
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Toward Use of Facial Thermal Features in Dynamic Assessment of Affect and Arousal Level
IEEE Transactions on Affective Computing, 2017Co-Authors: Masood Mehmood Khan, Robert D. Ward, Michael InglebyAbstract:Automated assessment of affect and arousal level can help psychologists and psychiatrists in clinical diagnoses; and may enable affect-aware robot-human interaction. This work identifies major difficulties in automating affect and arousal assessment and attempts to overcome some of them. We first analyze thermal infrared images and examine how changes in affect and/or arousal level would cause hæmodynamic variations, concentrated along certain facial muscles. These concentrations are used to measure affect/arousal induced facial thermal variations. In step-1 of a 2-step pattern recognition schema, `between-affect' and `between-arousal-level' variations are used to derive facial thermal features as Principal Components (PCs) of the facial thermal measurements. The most influential of these PCs are used to cluster the feature space for different affects and subsequently assign a set of thermal features to an affect cluster. In step-2, affect clusters are partitioned into high, medium and mild arousal levels. The distance between a test Face Vector and the centroids of sub-clusters at three arousal levels belonging to a single affective state, identified from step-1, is used to determine the arousal level of the identified affective state.
