Marcelo Bertalmío

Simultaneous structure and texture image inpainting

An algorithm for the simultaneous filling-in of texture and structure in regions of missing image information is presented in this paper. The basic idea is to first decompose the image into the sum of two functions with different basic characteristics, and then reconstruct each one of these functions separately with structure and texture filling-in algorithms. The first function used in the decomposition is of bounded variation, representing the underlying image structure, while the second function captures the texture and possible noise. The region of missing information in the bounded variation image is reconstructed using image inpainting algorithms, while the same region in the texture image is filled-in with texture synthesis techniques. The original image is then reconstructed adding back these two sub-images. The novel contribution of this paper is then in the combination of these three previously developed components, image decomposition with inpainting and texture synthesis, which permits the simultaneous use of filling-in algorithms that are suited for different image characteristics. Examples on real images show the advantages of this proposed approach.

Navier-stokes, fluid dynamics, and image and video inpainting

Image inpainting involves filling in part of an image or video using information from the surrounding area. Applications include the restoration of damaged photographs and movies and the removal of selected objects. We introduce a class of automated methods for digital inpainting. The approach uses ideas from classical fluid dynamics to propagate isophote lines continuously from the exterior into the region to be inpainted. The main idea is to think of the image intensity as a stream function for a two-dimensional incompressible flow. The Laplacian of the image intensity plays the role of the vorticity of the fluid; it is transported into the region to be inpainted by a vector field defined by the stream function. The resulting algorithm is designed to continue isophotes while matching gradient vectors at the boundary of the inpainting region. The method is directly based on the Navier-Stokes equations for fluid dynamics, which has the immediate advantage of well-developed theoretical and numerical results. This is a new approach for introducing ideas from computational fluid dynamics into problems in computer vision and image analysis.

Filling-in by joint interpolation of vector fields and gray levels

A variational approach for filling-in regions of missing data in digital images is introduced. The approach is based on joint interpolation of the image gray levels and gradient/isophotes directions, smoothly extending in an automatic fashion the isophote lines into the holes of missing data. This interpolation is computed by solving the variational problem via its gradient descent flow, which leads to a set of coupled second order partial differential equations, one for the gray-levels and one for the gradient orientations. The process underlying this approach can be considered as an interpretation of the Gestaltists principle of good continuation. No limitations are imposed on the topology of the holes, and all regions of missing data can be simultaneously processed, even if they are surrounded by completely different structures. Applications of this technique include the restoration of old photographs and removal of superimposed text like dates, subtitles, or publicity. Examples of these applications are given. We conclude the paper with a number of theoretical results on the proposed variational approach and its corresponding gradient descent flow.

Structure and texture filling-in of missing image blocks in wireless transmission and compression applications

An approach for filling-in blocks of missing data in wireless image transmission is presented. When compression algorithms such as JPEG are used as part of the wireless transmission process, images are first tiled into blocks of 8 x 8 pixels. When such images are transmitted over fading channels, the effects of noise can destroy entire blocks of the image. Instead of using common retransmission query protocols, we aim to reconstruct the lost data using correlation between the lost block and its neighbors. If the lost block contained structure, it is reconstructed using an image inpainting algorithm, while texture synthesis is used for the textured blocks. The switch between the two schemes is done in a fully automatic fashion based on the surrounding available blocks. The performance of this method is tested for various images and combinations of lost blocks. The viability of this method for image compression, in association with lossy JPEG, is also discussed.

A Comprehensive Framework for Image Inpainting

Inpainting is the art of modifying an image in a form that is not detectable by an ordinary observer. There are numerous and very different approaches to tackle the inpainting problem, though as explained in this paper, the most successful algorithms are based upon one or two of the following three basic techniques: copy-and-paste texture synthesis, geometric partial differential equations (PDEs), and coherence among neighboring pixels. We combine these three building blocks in a variational model, and provide a working algorithm for image inpainting trying to approximate the minimum of the proposed energy functional. Our experiments show that the combination of all three terms of the proposed energy works better than taking each term separately, and the results obtained are within the state-of-the-art.

Inpainting surface holes

An algorithm for filling-in surface holes is introduced in this paper. The basic idea is to represent the surface of interest in implicit form, and fill-in the holes with a system of geometric partial differential equations derived from image inpainting algorithms. The framework and examples with synthetic and real data are presented.

Morphing active contours

A method for deforming curves in a given image to a desired position in a second image is introduced. The algorithm is based on deforming the first image toward the second one via a partial differential equation (PDE), while tracking the deformation of the curves of interest in the first image with an additional, coupled PDE; both the images and the curves on the frame/slices of interest are used for tracking. The technique can be applied to object tracking and sequential segmentation. The topology of the deforming curve can change without any special topology handling procedures added to the scheme. This permits, for example, the automatic tracking of scenes where, due to occlusions, the topology of the objects of interest changes from frame to frame. In addition, this work introduces the concept of projecting velocities to obtain systems of coupled PDEs for image analysis applications. We show examples for object tracking and segmentation of electronic microscopy.

Video inpainting of occluding and occluded objects

We present a basic technique to fill-in missing parts of a video sequence taken from a static camera. Two important cases are considered. The first case is concerned with the removal of non-stationary objects that occlude stationary background. We use a priority based spatio-temporal synthesis scheme for inpainting the stationary background. The second and more difficult case involves filling-in moving objects when they are partially occluded. For this, we propose a priority scheme to first inpaint the occluded moving objects and then fill-in the remaining area with stationary background using the method proposed for the first case. We use as input an optical-flow based mask, which tells if an undamaged pixel is moving or is stationary. The moving object is inpainted by copying patches from undamaged frames, and this copying is independent of the background of the moving object in either frame. This work has applications in a variety of different areas, including video special effects and restoration and enhancement of damaged videos. The examples shown in the paper illustrate these ideas.

Perceptual Color Correction Through Variational Techniques

In this paper, we present a discussion about perceptual-based color correction of digital images in the framework of variational techniques. We propose a novel image functional whose minimization produces a perceptually inspired color enhanced version of the original. The variational formulation permits a more flexible local control of contrast adjustment and attachment to data. We show that a numerical implementation of the gradient descent technique applied to this energy functional coincides with the equation of automatic color enhancement (ACE), a particular perceptual-based model of color enhancement. Moreover, we prove that a numerical approximation of the Euler-Lagrange equation reduces the computational complexity of ACE from O(N2) to O(NlogN), where N is the total number of pixels in the image

Issues About Retinex Theory and Contrast Enhancement

AbstractWe present an interpretation of Land’s Retinex theory that we show to be consistent with the original formulation. The proposed model relies on the computation of the expectation value of a suitable random variable weighted with a kernel function, thus the name Kernel-Based Retinex (KBR) for the corresponding algorithm. KBR shares the same intrinsic characteristics of the original Retinex: it can reduce the effect of a color cast and enhance details in low-key images but, since it can only increase pixel intensities, it is not able to enhance over-exposed pictures. Comparing the analytical structure of KBR with that of a recent variational model of color image enhancement, we are able to perform an analysis of the action of KBR on contrast, showing the need to anti-symmetrize its equation in order to produce a two-sided contrast modification, able to enhance both under and over-exposed pictures. The anti-symmetrized KBR equations show clear correspondences with other existing color correction models, in particular ACE, whose relationship with Retinex has always been difficult to clarify. Finally, from an image processing point of view, we mention that both KBR and its antisymmetric version are free from the chromatic noise due to the use of paths in the original Retinex implementation and that they can be suitably approximated in order to reduce their computational complexity from