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Reconstruction of catadioptric omnidirectional images using dual alternating total variation minimization

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Abstract

This paper discusses the possibility to extend and apply the conventional two dimensional recovering images from blurry and noisy observation with the total variation regularization method to the catadioptric images. The principal in this special method is the stabilization of dual alternating minimization. The latter introduces two auxiliary half quadratic variables to transfer the system out of the ill-posed term. The main contribution of this paper is the use of the inverse stereographic projection and the spherical harmonics in order to adapt this proposed deconvolution with catadioptric omnidirectional images. The projection on the unit sphere of the omnidirectional image, is one way to alleviate the problem of the heterogeneous resolution and the negative effects of anamorphosis. In both anisotropic and isotropic deconvolutions, the experimental results conducted on synthetic as well as captured catadioptric omnidirectional images which are subject to various effects, confirm the performance of the proposed method to restore such images impaired by the blur and noise. Compared with several state-of-the-art approaches, the images resulted can achieve up to an acceptable and higher level of deconvolution quality.

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Acknowledgements

This research was supported by the Laboratory of Inverse Problems, Modeling, Information and Systems, University of Guelma. The author is indebted to his coauthors: A. Boukrouche and L. Boubchir for their encouragements and suggestions. Special acknowledgement is due to the former CREA (Caen) research labs for making available a set of images (Fig. 3b, c). Big thanks and a warm dedication to O. Elkadmiri for providing us with the synthetic image (Fig. 3a) and counselling us on restoration.

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Authors and Affiliations

  1. Laboratory of Inverse Problems, Modelling, Information and Systems, University 8 Mai 1945 Guelma, PO Box 401, 24000, Guelma, Algeria

    Soraya Zenati & Abdelhani Boukrouche

  2. Department of Computer Sciences, Badji Mokhtar University, PO Box 12, 23000, Annaba, Algeria

    Soraya Zenati

  3. LIASD research Lab., University of Paris 8, 2 rue de la Liberté, 93526, Saint-Denis, France

    Larbi Boubchir

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  1. Soraya Zenati
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  2. Abdelhani Boukrouche
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Correspondence to Abdelhani Boukrouche.

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Zenati, S., Boukrouche, A. & Boubchir, L. Reconstruction of catadioptric omnidirectional images using dual alternating total variation minimization. Evolving Systems 10, 707–723 (2019). https://doi.org/10.1007/s12530-018-9257-5

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