Fabrice Nonez - Academia.edu (original) (raw)
Papers by Fabrice Nonez
computer vision and pattern recognition, Feb 1, 2019
In computer vision, the gradient and Laplacian of an image are used in different applications, su... more In computer vision, the gradient and Laplacian of an image are used in different applications, such as edge detection, feature extraction, and seamless image cloning. Computing the gradient of an image is straightforward since numerical derivatives are available in most computer vision toolboxes. However, the reverse problem is more difficult, since computing an image from its gradient requires to solve the Laplacian equation (also called Poisson equation). Current discrete methods are either slow or require heavy parallel computing. The objective of this paper is to present a novel fast and robust method of solving the image gradient or Laplacian with minimal error, which can be used for gradient-domain editing. By using a single convolution based on a numerical Green's function, the whole process is faster and straightforward to implement with different computer vision libraries. It can also be optimized on a GPU using fast Fourier transforms and can easily be generalized for an n-dimension image. The tests show that, for images of resolution 801x1200, the proposed GFC can solve 100 Laplacian in parallel in around 1.0 milliseconds (ms). This is orders of magnitude faster than our nearest competitor which requires 294ms for a single image. Furthermore, we prove mathematically and demonstrate empirically that the proposed method is the least-error solver for gradient domain editing. The developed method is also validated with examples of Poisson blending, gradient removal, and the proposed gradient domain merging (GDM). Finally, we present how the GDM can be leveraged in future works for convolutional neural networks (CNN).
ArXiv, 2019
In computer vision, the gradient and Laplacian of an image are used in different applications, su... more In computer vision, the gradient and Laplacian of an image are used in different applications, such as edge detection, feature extraction, and seamless image cloning. Computing the gradient of an image is straightforward since numerical derivatives are available in most computer vision toolboxes. However, the reverse problem is more difficult, since computing an image from its gradient requires to solve the Laplacian equation, also called Poisson equation. Current discrete methods are either slow or require heavy parallel computing. The objective of this paper is to present a novel fast and robust method of solving the image gradient or Laplacian with minimal error, which can be used for gradient domain editing. By using a single convolution based on a numerical Green's function, the whole process is faster and straightforward to implement with different computer vision libraries. It can also be optimized on a GPU using fast Fourier transforms and can easily be generalized for a...
ArXiv, 2018
In Computer Vision, edge detection is one of the favored approaches for feature and object detect... more In Computer Vision, edge detection is one of the favored approaches for feature and object detection in images since it provides information about their objects boundaries. Other region-based approaches use probabilistic analysis such as clustering and Markov random fields, but those methods cannot be used to analyze edges and their interaction. In fact, only image segmentation can produce regions based on edges, but it requires thresholding by simply separating the regions into binary in-out information. Hence, there is currently a gap between edge-based and region-based algorithms, since edges cannot be used to study the properties of a region and vice versa. The objective of this paper is to present a novel spatial probability analysis that allows determining the probability of inclusion inside a set of partial contours (strokes). To answer this objective, we developed a new approach that uses electromagnetic convolutions and repulsion optimization to compute the required probabi...
Dans ce mémoire, nous travaillons sur les ensembles nodaux de combinaisons de fonctions propres d... more Dans ce mémoire, nous travaillons sur les ensembles nodaux de combinaisons de fonctions propres de ∆, le laplacien, sur des variétés spéciales. Soit M λ l'espace engendré par les fonctions propres de valeurs propres au plus λ. On démontrera que si u ∈ M λ sur la variété S n munie de sa métrique naturelle, alors le nombre total de Betti de u −1 (0) est d'ordre λ n 2. Nous obtiendrons un résultat similaire pour T n , le tore carré plat, lorsque n = 1, 2, 4 ou 8. Pour les autres dimensions, la borne sera de la forme O(λ 2n−1 2). Cela est fortement relié au théorème de Courant, qui traite du nombre de Betti zéro du complément de u −1 (0), l'ensemble nodal. Avec la loi de Weyl, on remarque que les bornes obtenues peuvent être vues comme une généralisation. Afin de tout démontrer, on utilisera des outils de diverses branches des mathématiques, notamment les résultats de Milnor sur les polynômes réels.
computer vision and pattern recognition, Feb 1, 2019
In computer vision, the gradient and Laplacian of an image are used in different applications, su... more In computer vision, the gradient and Laplacian of an image are used in different applications, such as edge detection, feature extraction, and seamless image cloning. Computing the gradient of an image is straightforward since numerical derivatives are available in most computer vision toolboxes. However, the reverse problem is more difficult, since computing an image from its gradient requires to solve the Laplacian equation (also called Poisson equation). Current discrete methods are either slow or require heavy parallel computing. The objective of this paper is to present a novel fast and robust method of solving the image gradient or Laplacian with minimal error, which can be used for gradient-domain editing. By using a single convolution based on a numerical Green's function, the whole process is faster and straightforward to implement with different computer vision libraries. It can also be optimized on a GPU using fast Fourier transforms and can easily be generalized for an n-dimension image. The tests show that, for images of resolution 801x1200, the proposed GFC can solve 100 Laplacian in parallel in around 1.0 milliseconds (ms). This is orders of magnitude faster than our nearest competitor which requires 294ms for a single image. Furthermore, we prove mathematically and demonstrate empirically that the proposed method is the least-error solver for gradient domain editing. The developed method is also validated with examples of Poisson blending, gradient removal, and the proposed gradient domain merging (GDM). Finally, we present how the GDM can be leveraged in future works for convolutional neural networks (CNN).
ArXiv, 2019
In computer vision, the gradient and Laplacian of an image are used in different applications, su... more In computer vision, the gradient and Laplacian of an image are used in different applications, such as edge detection, feature extraction, and seamless image cloning. Computing the gradient of an image is straightforward since numerical derivatives are available in most computer vision toolboxes. However, the reverse problem is more difficult, since computing an image from its gradient requires to solve the Laplacian equation, also called Poisson equation. Current discrete methods are either slow or require heavy parallel computing. The objective of this paper is to present a novel fast and robust method of solving the image gradient or Laplacian with minimal error, which can be used for gradient domain editing. By using a single convolution based on a numerical Green's function, the whole process is faster and straightforward to implement with different computer vision libraries. It can also be optimized on a GPU using fast Fourier transforms and can easily be generalized for a...
ArXiv, 2018
In Computer Vision, edge detection is one of the favored approaches for feature and object detect... more In Computer Vision, edge detection is one of the favored approaches for feature and object detection in images since it provides information about their objects boundaries. Other region-based approaches use probabilistic analysis such as clustering and Markov random fields, but those methods cannot be used to analyze edges and their interaction. In fact, only image segmentation can produce regions based on edges, but it requires thresholding by simply separating the regions into binary in-out information. Hence, there is currently a gap between edge-based and region-based algorithms, since edges cannot be used to study the properties of a region and vice versa. The objective of this paper is to present a novel spatial probability analysis that allows determining the probability of inclusion inside a set of partial contours (strokes). To answer this objective, we developed a new approach that uses electromagnetic convolutions and repulsion optimization to compute the required probabi...
Dans ce mémoire, nous travaillons sur les ensembles nodaux de combinaisons de fonctions propres d... more Dans ce mémoire, nous travaillons sur les ensembles nodaux de combinaisons de fonctions propres de ∆, le laplacien, sur des variétés spéciales. Soit M λ l'espace engendré par les fonctions propres de valeurs propres au plus λ. On démontrera que si u ∈ M λ sur la variété S n munie de sa métrique naturelle, alors le nombre total de Betti de u −1 (0) est d'ordre λ n 2. Nous obtiendrons un résultat similaire pour T n , le tore carré plat, lorsque n = 1, 2, 4 ou 8. Pour les autres dimensions, la borne sera de la forme O(λ 2n−1 2). Cela est fortement relié au théorème de Courant, qui traite du nombre de Betti zéro du complément de u −1 (0), l'ensemble nodal. Avec la loi de Weyl, on remarque que les bornes obtenues peuvent être vues comme une généralisation. Afin de tout démontrer, on utilisera des outils de diverses branches des mathématiques, notamment les résultats de Milnor sur les polynômes réels.