This article describes an implementation of the optical flow estimation method introduced by Zach, Pock and Bischof in 2007. This method is based on the minimization of a functional containing a data term using the L 1 norm and a regularization term using the total variation of the flow. The main feature of this formulation is that it allows discontinuities in the flow field, while being more robust to noise than the classical approach by Horn and Schunck. The algorithm is an efficient numerical scheme, which solves a relaxed version of the problem by alternate minimization. Source CodeA C implementation of this algorithm is provided. The source code and an online demo are accessible at the web page of this article 1 .

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ABSTRACT:The increasing availability of high resolution stereo images from Earth observation satellites has boosted the development of tools for producing 3D elevation models. The objective of these tools is to produce digital elevation models of very large areas with minimal human intervention. The development of these tools has been shaped by the constraints of the remote sensing acquisition, for example, using ad hoc stereo matching tools to deal with the pushbroom image geometry. However, this specialization has also created a gap with respect to the fields of computer vision and image processing, where these constraints are usually factored out. In this work we propose a fully automatic and modular stereo pipeline to produce digital elevation models from satellite images. The aim of this new pipeline, called Satellite Stereo Pipeline and abbreviated as s2p, is to use (and test) off-the-shelf computer vision tools while abstracting from the complexity associated to satellite imaging. To this aim, images are cut in small tiles for which we proved that the pushbroom geometry is very accurately approximated by the pinhole model. These tiles are then processed with standard stereo image rectification and stereo matching tools. The specifics of satellite imaging such as pointing accuracy refinement, estimation of the initial elevation from SRTM data, and geodetic coordinate systems are handled transparently by s2p. We demonstrate the robustness of our approach on a large database of satellite images and by providing an online demo of s2p.Figure 1: 3D point clouds automatically generated from Pléiades stereo datasets, without any manual intervention, with the s2p stereo pipeline. Its implementation can be tested online through a web browser.

The seminal work of Horn and Schunck is the first variational method for optical flow estimation. It introduced a novel framework where the optical flow is computed as the solution of a minimization problem. From the assumption that pixel intensities do not change over time, the optical flow constraint equation is derived. This equation relates the optical flow with the derivatives of the image. There are infinitely many vector fields that satisfy the optical flow constraint, thus the problem is ill-posed. To overcome this problem, Horn and Schunck introduced an additional regularity condition that restricts the possible solutions. Their method minimizes both the optical flow constraint and the magnitude of the variations of the flow field, producing smooth vector fields. One of the limitations of this method is that, typically, it can only estimate small motions. In the presence of large displacements, this method fails when the gradient of the image is not smooth enough. In this work, we describe an implementation of the original Horn and Schunck method and also introduce a multi-scale strategy in order to deal with larger displacements. For this multi-scale strategy, we create a pyramidal structure of downsampled images and change the optical flow constraint equation with a nonlinear formulation. In order to tackle this nonlinear formula, we linearize it and solve the method iteratively in each scale. In this sense, there are two common approaches: one that computes the motion increment in the iterations; or the one we follow, that computes the full flow during the iterations. The solutions are incrementally refined over the scales. This pyramidal structure is a standard tool in many optical flow methods. Source Code A standalone ANSI C implementation is available 1. This file contains two main programs: horn schunck classic.c, which implements the original Horn and Schunck method; and the implementation of the multi-scale approach, in file horn schunck pyramidal.c. This latter implementation is best suited for general image sequences.

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The centroid method for the correction of turbulence consists in computing the Karcher-Fréchet mean of the sequence of input images. The direction of deformation between a pair of images is determined by the optical flow. A distinguishing feature of the centroid method is that it can produce useful results from an arbitrarily small set of input images. Source CodeThe source code and a online demo are accessible at the IPOL web page of this article 1 .

The integral image representation is a remarkable idea that permits to evaluate the sum of image values over rectangular regions of the image with four operations, regardless of the size of the region. It was first proposed under the name of summed area table in the computer graphics community by Crow'84, in order to efficiently filter texture maps. It was later popularized in the computer vision community by Viola & Jones'04 with its use in their real-time object detection framework. In this article we describe the integral image algorithm and study its application in the context of block matching. We investigate tradeoffs and the limits of the performance gain with respect to exhaustive block matching.

The gradient of images can be directly edited to perform useful operations; this is called gradientbased image processing or Poisson editing. For example operations such as seamless cloning, contrast enhancement, texture flattening or seamless tiling can be performed in a very simple and efficient way by combining/modifying the image gradients. In the present work we will describe the Poisson image editing method, and review the contributions that have been made since it was proposed in 2003. In addition the integration problem will be discussed and analyzed, both from the theoretical and numerical points of view. Two different numerical implementations will be discussed, the first one uses discrete versions of differential operators to convert the problem into a sparse linear system of equations, while the second one is based on Fourier transform properties. Source CodeThe Octave/Matlab source code, the code documentation, and the online demo are accessible at the IPOL web page of this article 1 and usage instruction are included in the README.txt file of the compressed archive.