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219
Fragment-based image completion
- ACM TRANS. ON GRAPHICS. SPECIAL ISSUE: PROC. OF ACM SIGGRAPH
, 2003
"... We present a new method for completing missing parts caused by the removal of foreground or background elements from an image. Our goal is to synthesize a complete, visually plausible and coherent image. The visible parts of the image serve as a training set to infer the unknown parts. Our method it ..."
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Cited by 135 (4 self)
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We present a new method for completing missing parts caused by the removal of foreground or background elements from an image. Our goal is to synthesize a complete, visually plausible and coherent image. The visible parts of the image serve as a training set to infer the unknown parts. Our method iteratively approximates the unknown regions and composites adaptive image fragments into the image. Values of an inverse matte are used to compute a confidence map and a level set that direct an incremental traversal within the unknown area from high to low confidence. In each step, guided by a fast smooth approximation, an image fragment is selected from the most similar and frequent examples. As the selected fragments are composited, their likelihood increases along with the mean confidence of the image, until reaching a complete image. We demonstrate our method by completion of photographs and paintings.
Euler's Elastica And Curvature Based Inpaintings
- SIAM J. Appl. Math
, 2002
"... Image inpainting is a special image restoration problem for which image prior models play a crucial role. Euler's elastica was first introduced by Mumford [21] to computer vision as a prior curve model. By functionalizing the elastica energy, Masnou and Morel [19] proposed an elastica based var ..."
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Cited by 114 (26 self)
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Image inpainting is a special image restoration problem for which image prior models play a crucial role. Euler's elastica was first introduced by Mumford [21] to computer vision as a prior curve model. By functionalizing the elastica energy, Masnou and Morel [19] proposed an elastica based variational inpainting model. The current paper is intended to contribute to the development of its mathematical foundation, and the study of its properties and connections to the earlier works of Bertalmio, Sapiro, Caselles, and Ballester [2] and Chan and Shen [6, 7]. A computational scheme based on numerical PDEs is presented, which allows the handling of topologically complex inpainting domains.
A framelet-based image inpainting algorithm
- Applied and Computational Harmonic Analysis
"... Abstract. Image inpainting is a fundamental problem in image processing and has many applications. Motivated by the recent tight frame based methods on image restoration in either the image or the transform domain, we propose an iterative tight frame algorithm for image inpainting. We consider the c ..."
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Cited by 90 (40 self)
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Abstract. Image inpainting is a fundamental problem in image processing and has many applications. Motivated by the recent tight frame based methods on image restoration in either the image or the transform domain, we propose an iterative tight frame algorithm for image inpainting. We consider the convergence of this framelet-based algorithm by interpreting it as an iteration for minimizing a special functional. The proof of the convergence is under the framework of convex analysis and optimization theory. We also discuss the relationship of our method with other wavelet-based methods. Numerical experiments are given to illustrate the performance of the proposed algorithm. Key words. Tight frame, inpainting, convex analysis 1. Introduction. The problem of inpainting [2] occurs when part of the pixel data in a picture is missing or over-written by other means. This arises for example in restoring ancient drawings, where a portion of the picture is missing or damaged due to aging or scratch; or when an image is transmitted through a noisy channel. The task of inpainting is to recover the missing region from the incomplete data observed. Ideally, the restored image should possess shapes and patterns consistent
Digital inpainting based on the Mumford-Shah-Euler image model
- European J. Appl. Math
, 2002
"... Abstract. Image inpainting is an image restoration problem, in which image models play a critical role, as demonstrated by Chan, Kang and Shen’s recent inpainting schemes based on the bounded variation [10] and the elastica [9] image models. In the present paper, we propose two novel inpainting mode ..."
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Cited by 81 (23 self)
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Abstract. Image inpainting is an image restoration problem, in which image models play a critical role, as demonstrated by Chan, Kang and Shen’s recent inpainting schemes based on the bounded variation [10] and the elastica [9] image models. In the present paper, we propose two novel inpainting models based on the Mumford-Shah image model [37], and its high order correction — the Mumford-Shah-Euler image model. We also present their efficient numerical realization based on the ¡ and De Giorgi [18]. Key words. Inpainting, Bayesian, image model, Euler’s elastica, ¡
Recent developments in total variation image restoration
- In Mathematical Models of Computer Vision
, 2005
"... ABSTRACT Since their introduction in a classic paper by Rudin, Osher and Fatemi [26], total variation minimizing models have become one of the most popular and successful methodology for image restoration. More recently, there has been a resurgence of interest and exciting new developments, some ext ..."
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Cited by 71 (2 self)
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ABSTRACT Since their introduction in a classic paper by Rudin, Osher and Fatemi [26], total variation minimizing models have become one of the most popular and successful methodology for image restoration. More recently, there has been a resurgence of interest and exciting new developments, some extending the applicabilities to inpainting, blind deconvolution and vector-valued images, while others offer improvements in better preservation of contrast, geometry and textures, in ameliorating the staircasing effect, and in exploiting the multiscale nature of the models. In addition, new computational methods have been proposed with improved computational speed and robustness. We shall review some of these recent developments. 1
Learning How to Inpaint from Global Image Statistics
"... Inpainting is the problem of filling-in holes in images. Considerable progress has been made by techniques that use the immediate boundary of the hole and some prior information on images to solve this problem. These algorithms successfully solve the local inpainting problem but they must, by defini ..."
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Cited by 64 (1 self)
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Inpainting is the problem of filling-in holes in images. Considerable progress has been made by techniques that use the immediate boundary of the hole and some prior information on images to solve this problem. These algorithms successfully solve the local inpainting problem but they must, by definition, give the same completion to any two holes that have the same boundary, even when the rest of the image is vastly different.
Non-local Regularization of Inverse Problems
, 2008
"... This article proposes a new framework to regularize linear inverse problems using the total variation on non-local graphs. This nonlocal graph allows to adapt the penalization to the geometry of the underlying function to recover. A fast algorithm computes iteratively both the solution of the regul ..."
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Cited by 56 (3 self)
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This article proposes a new framework to regularize linear inverse problems using the total variation on non-local graphs. This nonlocal graph allows to adapt the penalization to the geometry of the underlying function to recover. A fast algorithm computes iteratively both the solution of the regularization process and the non-local graph adapted to this solution. We show numerical applications of this method to the resolution of image processing inverse problems such as inpainting, super-resolution and compressive sampling.
Inpainting and zooming using sparse representations
- The Computer Journal
"... Representing the image to be inpainted in an appropriate sparse representation dictionary, and combining elements from Bayesian statistics and modern harmonic analysis, we introduce an expectation maximization (EM) algorithm for image inpainting and interpolation. From a statistical point of view, t ..."
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Cited by 55 (8 self)
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Representing the image to be inpainted in an appropriate sparse representation dictionary, and combining elements from Bayesian statistics and modern harmonic analysis, we introduce an expectation maximization (EM) algorithm for image inpainting and interpolation. From a statistical point of view, the inpainting/interpolation can be viewed as an estimation problem with missing data. Toward this goal, we propose the idea of using the EM mechanism in a Bayesian framework, where a sparsity promoting prior penalty is imposed on the reconstructed coefficients. The EM framework gives a principled way to establish formally the idea that missing samples can be recovered/ interpolated based on sparse representations. We first introduce an easy and efficient sparserepresentation-based iterative algorithm for image inpainting. Additionally, we derive its theoretical convergence properties. Compared to its competitors, this algorithm allows a high degree of flexibility to recover different structural components in the image (piecewise smooth, curvilinear, texture, etc.). We also suggest some guidelines to automatically tune the regularization parameter.
Data processing algorithms for generating textured 3D building facade meshes from laser scans and camera images
- IJCV
, 2002
"... Abstract. In this paper, we develop a set of data processing algorithms for generating textured facade meshes of cities from a series of vertical 2D surface scans and camera images, obtained by a laser scanner and digital camera while driving on public roads under normal traffic conditions. These pr ..."
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Cited by 54 (3 self)
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Abstract. In this paper, we develop a set of data processing algorithms for generating textured facade meshes of cities from a series of vertical 2D surface scans and camera images, obtained by a laser scanner and digital camera while driving on public roads under normal traffic conditions. These processing steps are needed to cope with imperfections and non-idealities inherent in laser scanning systems such as occlusions and reflections from glass surfaces. The data is divided into easy-to-handle quasi-linear segments corresponding to approximately straight driving direction and sequential topological order of vertical laser scans; each segment is then transformed into a depth image. Dominant building structures are detected in the depth images, and points are classified into foreground and background layers. Large holes in the background layer, caused by occlusion from foreground layer objects, are filled in by planar or horizontal interpolation. The depth image is further processed by removing isolated points and filling remaining small holes. The foreground objects also leave holes in the texture of building facades, which are filled by horizontal and vertical interpolation in low frequency regions, or by a copy-paste method otherwise. We apply the above steps to a large set of data of downtown Berkeley with several million 3D points, in order to obtain texture-mapped 3D models.
Variational PDE models in image processing
, 2002
"... This paper is based on a plenary presentation given by Tony F. Chan at the 2002 Joint Mathematical Meeting, San Diego, and has been supported in part by NSF under grant numbers DMS-9973341 (Chan), DMS-0202565 (Shen), and ITR-0113439 (Vese), by ONR under N00014-02-1-0015 (Chan), and by NIH under NIH- ..."
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Cited by 46 (11 self)
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This paper is based on a plenary presentation given by Tony F. Chan at the 2002 Joint Mathematical Meeting, San Diego, and has been supported in part by NSF under grant numbers DMS-9973341 (Chan), DMS-0202565 (Shen), and ITR-0113439 (Vese), by ONR under N00014-02-1-0015 (Chan), and by NIH under NIH-P20MH65166 (Chan and Vese). For the preprints and reprints mentioned in this paper, please visit our web site at: www.math.ucla.edu/~imagers. Chan and Vese are with the Department of Mathematics, UCLA, Los Angeles, CA 90095, fchan, lveseg@math.ucla.edu; Shen is with the School of Mathematics, University of Minnesota, Minneapolis, MN 55455, jhshen@math.umn.edu
