Derivative Half Gaussian Kernels and Shock Filter

Baptiste Magnier (1) , Vincent Noblet (1) , Adrien Voisin (1) , Dylan Legouestre (1)

1 LGI2P - Laboratoire de Génie Informatique et Ingénierie de Production

Shock filter represents an important family in the field of nonlinear Partial Differential Equations (PDEs) models for image restoration and enhancement. Commonly, the smoothed second order derivative of the image assists this type of method in the deblurring mechanism. This paper presents the advantages to insert information issued of oriented half Gaussian kernels in a shock filter process. Edge directions assist to preserve contours whereas the gradient direction allow to enhance and deblur images. For this purpose, the two edge directions are extracted by the oriented half kernels, preserving and enhancing well corner points and object contours as well as small objects. The proposed approach is compared to 7 other PDE techniques, presenting its robust-ness and reliability, without creating a grainy effect around edges. Since 1960, digital images may simply be deblurred by combining the difference between an original image I 0 and ∆I: a blurred version of this same image. Usually, ∆I corresponds to a blur process equivalent to the heat equation or a convolution of I 0 with an isotropic Gaussian. This original theory proposed by Gabor is proportional to using the Laplacian operator [7]. Thus, a simplest manner to remove blur in an image remains the equation: ∂I ∂t = I 0 − α · ∆I, (1) where t represents the time or the observation scale and α < 1 is a little scalar to control the deblurring. This process is equivalent to the inverse heat equation. However, this technique is not stable because the procedure blows up after several iterations and generates an unusable image [7]. To improve eq. 1, rather than applying a global operator on all the image, the main idea is to iterate local operator at level of each pixel. Nonlinear Partial Differential Equations (PDEs) may achieve this task [7,2], practicing anisotropic diffusions of pixel information in the image. Indeed, PDEs belong to one of the most important part of mathematical analysis and are closely related to the physical world. In this context, images are considered as evolving functions of time and a regularized image can be seen as a version of the original image at a special scale.

Mots clés: Half gaussian kernels; Shock filter; PDE

Domaines: Vision par ordinateur et reconnaissance de formes [cs.CV]; Traitement des images [eess.IV]

Baptiste Magnier, Vincent Noblet, Adrien Voisin, Dylan Legouestre. Derivative Half Gaussian Kernels and Shock Filter. ACIVS 2018 - Advanced Concepts for Intelligent Vision Systems, Sep 2018, Poitiers, France. pp.584-597, ⟨10.1007/978-3-030-01449-0_49⟩. ⟨hal-01940267⟩