A new algorithm is proposed for removing large objects from digital images. The challenge is to fill in the hole that is left behind in a visually plausible way. In the past, this problem has been addressed by two classes of algorithms: 1) “texture synthesis” algorithms for generating large image regions from sample textures and 2) “inpainting ” techniques for filling in small image gaps. The former has been demonstrated for “textures”—repeating twodimensional patterns with some stochasticity; the latter focus on linear “structures ” which can be thought of as one-dimensional patterns, such as lines and object contours. This paper presents a novel and efficient algorithm that combines the advantages of these two approaches. We first note that exemplar-based texture synthesis contains the essential process required to replicate both texture and structure; the success of structure propagation, however, is highly dependent on the order in which the filling proceeds. We propose a best-first algorithm in which the confidence in the synthesized pixel values is propagated in a manner similar to the propagation of information in inpainting. The actual color values are computed using exemplar-based synthesis. In this paper, the simultaneous propagation of texture and structure information is achieved by a single, efficient algorithm. Computational efficiency is achieved by a block-based sampling process. A number of examples on real and synthetic images demonstrate the effectiveness of our algorithm in removing large occluding objects, as well as thin scratches. Robustness with respect to the shape of the manually selected target region is also demonstrated. Our results compare favorably to those obtained by existing techniques.

Figure 1: A seam is a connected path of low energy pixels in an image. On the left is the original image with one horizontal and one vertical seam. In the middle the energy function used in this example is shown (the magnitude of the gradient), along with the vertical and horizontal path maps used to calculate the seams. By automatically carving out seams to reduce image size, and inserting seams to extend it, we achieve content-aware resizing. The example on the top right shows our result of extending in one dimension and reducing in the other, compared to standard scaling on the bottom right. Effective resizing of images should not only use geometric constraints, but consider the image content as well. We present a simple image operator called seam carving that supports content-aware image resizing for both reduction and expansion. A seam is an optimal 8-connected path of pixels on a single image from top to bottom, or left to right, where optimality is defined by an image energy function. By repeatedly carving out or inserting seams in one direction we can change the aspect ratio of an image. By applying these operators in both directions we can retarget the image to a new size. The selection and order of seams protect the content of the image, as defined by the energy function. Seam carving can also be used for image content enhancement and object removal. We support various visual saliency measures for defining the energy of an image, and can also include user input to guide the process. By storing the order of seams in an image we create multi-size images, that are able to continuously change in real time to fit a given size.

The separation of image content into semantic parts plays a vital role in applications such as compression, enhancement, restoration, and more. In recent years several pioneering works suggested such a separation based on variational formulation, and others using independent component analysis and sparsity. This paper presents a novel method for separating images into texture and piecewise smooth (cartoon) parts, exploiting both the variational and the sparsity mechanisms. The method combines the Basis Pursuit Denoising (BPDN) algorithm and the Total-Variation (TV) regularization scheme. The basic idea presented in this paper is the use of two appropriate dictionaries, one for the representation of textures, and the other for the natural scene parts, assumed to be piecewise-smooth. Both dictionaries are chosen such that they lead to sparse representations over one type of image-content (either texture or piecewise smooth). The use of the BPDN with the two augmented dictionaries leads to the desired separation, along with noise removal as a by-product. As the need to choose proper dictionaries is generally hard, a TV regularization is employed to better direct the separation process and reduce ringing artifacts. We present a highly e#cient numerical scheme to solve the combined optimization problem posed in our model, and show several experimental results that validate the algorithm's performance.

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.

two intersecting lines (green) specified by the user, (c) intermediate result after propagating structure and texture information along the user-specified lines, and (d) final result after filling in the remaining unknown regions by texture propagation. In this paper, we introduce a novel approach to image completion, which we call structure propagation. In our system, the user manually specifies important missing structure information by extending a few curves or line segments from the known to the unknown regions. Our approach synthesizes image patches along these user-specified curves in the unknown region using patches selected around the curves in the known region. Structure propagation is formulated as a global optimization problem by enforcing structure and consistency constraints. If only a single curve is specified, structure propagation is solved using Dynamic Programming. When multiple intersecting curves are specified, we adopt the Belief Propagation algorithm to find the optimal patches. After completing structure propagation, we fill in the remaining unknown regions using patch-based texture synthesis. We show that our approach works well on a number of examples that are challenging to state-of-the-art techniques.

We study the robust estimation of missing regions in images and video using adaptive, sparse reconstructions. Our primary application is on missing regions of pixels containing textures, edges, and other image features that are not readily handled by prevalent estimation and recovery algorithms. We assume that we are given a linear transform that is expected to provide sparse decompositions over missing regions such that a portion of the transform coe#cients over missing regions are zero or close to zero. We adaptively determine these small magnitude coe#cients through thresholding, establish sparsity constraints, and estimate missing regions in images using information surrounding these regions. Unlike prevalent algorithms, our approach does not necessitate any complex preconditioning, segmentation, or edge detection steps, and it can be written as a sequence of denoising operations. We show that the region types we can e#ectively estimate in a mean squared error sense are those for which the given transform provides a close approximation using sparse nonlinear approximants. We show the nature of the constructed estimators and how these estimators relate to the utilized transform and its sparsity over regions of interest. The developed estimation framework is general, and can readily be applied to nonstationary signals with a suitable choice of linear transforms. Part I discusses fundamental issues, and Part II is devoted to adaptive algorithms with extensive simulation examples that demonstrate the power of the proposed techniques.

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.

Abstract. In this paper, we propose a new variational model for image denoising and decomposition, witch combines the total variation minimization model of Rudin, Osher and Fatemi from image restoration, with spaces of oscillatory functions, following recent ideas introduced by Meyer. The spaces introduced here are appropriate to model oscillatory patterns of zero mean, such as noise or texture. Numerical results of image denoising, image decomposition and texture discrimination are presented, showing that the new models decompose better a given image, possible noisy, into cartoon and oscillatory pattern of zero mean, than the standard ones. The present paper develops further the models previously introduced by the authors in Vese and Osher (Modeling textures with total variation minimization and oscillating patterns in image processing, UCLA CAM Report 02-19, May 2002, to appear in Journal of Scientific Computing, 2003). Other recent and related image decomposition models are also discussed.

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

This paper presents a novel method for separating images into texture and piecewise smooth parts. The proposed approach is based on a combination of the Basis Pursuit Denoising (BPDN) algorithm and the Total-Variation (TV) regularization scheme. The basic idea promoted in this paper is the use of two appropriate dictionaries, one for the representation of textures, and the other for the natural scene parts. Each dictionary is designed for sparse representation of a particular type of image-content (either texture or piecewise smooth). The use of BPDN with the two augmented dictionaries leads to the desired separation, along with noise removal as a by-product. As the need to choose a proper dictionary for natural scene is very hard, a TV regularization is employed to better direct the separation process. Experimental results validate the algorithm's performance.