Optimally isotropic Laplacian operator

Kamgar‐Parsi, B.; Rosenfeld, A.

doi:10.1109/83.791975

Cited by 59 publications

(27 citation statements)

References 7 publications

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“…The only anisotropic behavior of those filters is limited to the anisotropic response of the discrete Laplacian operator (Kamgar Parsi et al 1999). Most of the discrete Laplacian operators exhibit an anisotropic response to the edge with respect to x and y (i.e.…”

Section: Diffusion Equationmentioning

confidence: 99%

An Anisotropic Fourth-Order Diffusion Filter for Image Noise Removal

Hajiaboli

2010

Int J Comput Vis

136

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Fourth-order nonlinear diffusion filters used for image noise removal are mainly isotropic filters. It means that the spatially varying diffusivity determined by a diffusion function is applied on the image regardless of the orientation of its local features. However, the optimal choice of parameters in the numerical solver of these filters for having a minimal distortion of the image features results in forming speckle noise on the denoised image and a very slow convergence rate especially when the noise level is moderately high. In this paper, a new fourth-order nonlinear diffusion filter is introduced, which has an anisotropic behavior on the image features. In the proposed filter, it is shown that a suitable choice for a set of diffusivity functions to unevenly control the strength of the diffusion on the directions of the level set and gradient leads to a good edge preservation capability compared to the other diffusion or regularization filters. The comparison of the results obtained by the proposed filter with those of the other second and fourth-order filters shows that the proposed method produces a noticeable improvement in the quality of denoised images evaluated subjectively and quantitatively.

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Section: Diffusion Equationmentioning

confidence: 99%

An Anisotropic Fourth-Order Diffusion Filter for Image Noise Removal

Hajiaboli

2010

Int J Comput Vis

136

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“…Kernel k 3 originates from the numerical analysis field [23]. Kernel k 4 is common in the image processing community [21]. To analyze the isotropy of these kernels, we transformed them into Fourier domain with their spectral magnitude plotted in Fig.…”

Section: A Discretization Of Weighted Mean Curvaturementioning

confidence: 99%

Weighted mean curvature

Gong

Göksel

2019

Signal Processing

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In image processing tasks, spatial priors are essential for robust computations, regularization, algorithmic design and Bayesian inference. In this paper, we introduce weighted mean curvature (WMC) as a novel image prior and present an efficient computation scheme for its discretization in practical image processing applications. We first demonstrate the favorable properties of WMC, such as sampling invariance, scale invariance, and contrast invariance with Gaussian noise model; and we show the relation of WMC to area regularization. We further propose an efficient computation scheme for discretized WMC, which is demonstrated herein to process over 33.2 giga-pixels/second on GPU. This scheme yields itself to a convolutional neural network representation. Finally, WMC is evaluated on synthetic and real images, showing its superiority quantitatively to total-variation and mean curvature.

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“…A common solution in computer vision is then to use one or more edge detection algorithm to reduce the image information to be processed by the shape detection algorithm. The most used algorithms for the edge detection are the Robert's Cross operator [18], Sobel operator [19], laplacian of gaussian filter [20] and the Canny's edge detection algorithm [21]. The latter is the one that is selected in most real time applications such as those that will be implemented in the NOAH project.…”

Section: Autonomous Detection and Tracking Of Potential Poaching Eventsmentioning

confidence: 99%

The NOAH Project: Giving a Chance to Threatened Species in Africa with UAVs

Olivares-Méndez

Bissyandé

Kannan

et al. 2014

Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering

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Abstract. Organized crime now targets one of the most precious wealth in Africa, the wild life. The most affected by the poaching are the Big 5, whose survival requires attention and efforts from everyone, in accordance to his own expertise. Just as Noah 1 was tasked to save every species from the Genesis flood, we envision the NOAH Project to (re)make natural parks as a safe haven. This endeavor requires efficient and effective surveillance which is now facilitated by the use of UAVs. We take this approach further by proposing the use of ICT algorithms to automate surveillance. The proposed intelligent system could inspect a bigger area, recognize potential threats and be manage by non-expert users, reducing the expensive resources that are needed by developing countries to address the problem.

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Optimally isotropic Laplacian operator

Abstract: Laplacian operators used in the literature for digital image processing are not rotationally invariant. We examine the anisotropy of 3 x 3 Laplacian operators for images quantized in square pixels, and find the operator which has the minimum overall anisotropy.

Cited by 59 publications

References 7 publications

An Anisotropic Fourth-Order Diffusion Filter for Image Noise Removal

An Anisotropic Fourth-Order Diffusion Filter for Image Noise Removal

Weighted mean curvature

The NOAH Project: Giving a Chance to Threatened Species in Africa with UAVs

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