Adaptive structure tensors and their applications

The structure tensor, also known as second moment matrix or Förstner interest operator, is a very popular tool in image processing. Its purpose is the estimation of orientation and the local analysis of structure in general. It is based on the integration of data from a local neighborhood. Normally, this neighborhood is defined by a Gaussian window function and the structure tensor is computed by the weighted sum within this window. Some recently proposed methods, however, adapt the computation of the structure tensor to the image data. There are several ways how to do that. This article wants to give an overview of the different approaches, whereas the focus lies on the methods based on robust statistics and nonlinear diffusion. Furthermore, the dataadaptive structure tensors are evaluated in some applications. Here the main focus lies on optic flow estimation, but also texture analysis and corner detection are considered

Lucas/Kanade meets Horn/Schunck : combining local and global optic flow methods

Differential methods belong to the most widely used techniques for optic flow computation in image sequences. They can be classified into local methods such as the Lucas-Kanade technique or Bigün\u27s structure tensor method, and into global methods such as the Horn/Schunck approach and its extensions. Often local methods are more robust under noise, while global techniques yield dense flow fields. The goal of this paper is to contribute to a better understanding and the design of differential methods in four ways: (i) We juxtapose the role of smoothing/regularisation processes that are required in local and global differential methods for optic flow computation. (ii) This discussion motivates us to describe and evaluate a novel method that combines important advantages of local and global approaches: It yields dense flow fields that are robust against noise. (iii) Spatiotemproal and nonlinear extensions to this hybrid method are presented. (iv) We propose a simple confidence measure for optic flow methods that minimise energy functionals. It allows to sparsify a dense flow field gradually, depending on the reliability required for the resulting flow. Comparisons with experiments from the literature demonstrate the favourable performance of the proposed methods and the confidence measure

Highly accurate optic flow computation with theoretically justified warping

In this paper, we suggest a variational model for optic flow computation based on non-linearised and higher order constancy assumptions. Besides the common grey value constancy assumption, also gradient constancy, as well as the constancy of the Hessian and the Laplacian are proposed. Since the model strictly refrains from a linearisation of these assumptions, it is also capable to deal with large displacements. For the minimisation of the rather complex energy functional, we present an efficient numerical scheme employing two nested fixed point iterations. Following a coarse-to-fine strategy it turns out that there is a theoretical foundation of so-called warping techniques hitherto justified only on an experimental basis. Since our algorithm consists of the integration of various concepts, ranging from different constancy assumptions to numerical implementation issues, a detailed account of the effect of each of these concepts is included in the experimental section. The superior performance of the proposed method shows up by significantly smaller estimation errors when compared to previous techniques. Further experiments also confirm excellent robustness under noise and insensitivity to parameter variations

A multigrid platform for real-time motion computation with discontinuity-preserving variational methods

Variational methods are among the most accurate techniques for estimating the optic flow. They yield dense flow fields and can be designed such that they preserve discontinuities, allow to deal with large displacements and perform well under noise or varying illumination. However, such adaptations render the minimisation of the underlying energy functional very expensive in terms of computational costs: Typically, one or more large linear or nonlinear systems of equations have to be solved in order to obtain the desired solution. Consequently, variational methods are considered to be too slow for real-time performance. In our paper we address this problem in two ways: (i) We present a numerical framework based on bidirectional multigrid methods for accelerating a broad class of variational optic flow methods with different constancy and smoothness assumptions. In particular, discontinuity-preserving regularisation strategies are thereby in the focus of our work. (ii) We show by the examples of classical as well as more advanced variational techniques that real-time performance is possible - even for very complex optic flow models with high accuracy. Experiments show frame rates up to 63 dense flow fields per second for real-world image sequences of size 160 x 120 on a standard PC. Compared to classical iterative methods this constitutes a speedup of two to four orders of magnitude

Depth Estimation Using 2D RGB Images

Single image depth estimation is an ill-posed problem. That is, it is not mathematically possible to uniquely estimate the 3rd dimension (or depth) from a single 2D image. Hence, additional constraints need to be incorporated in order to regulate the solution space. As a result, in the first part of this dissertation, the idea of constraining the model for more accurate depth estimation by taking advantage of the similarity between the RGB image and the corresponding depth map at the geometric edges of the 3D scene is explored. Although deep learning based methods are very successful in computer vision and handle noise very well, they suffer from poor generalization when the test and train distributions are not close. While, the geometric methods do not have the generalization problem since they benefit from temporal information in an unsupervised manner. They are sensitive to noise, though. At the same time, explicitly modeling of a dynamic scenes as well as flexible objects in traditional computer vision methods is a big challenge. Considering the advantages and disadvantages of each approach, a hybrid method, which benefits from both, is proposed here by extending traditional geometric models’ abilities to handle flexible and dynamic objects in the scene. This is made possible by relaxing geometric computer vision rules from one motion model for some areas of the scene into one for every pixel in the scene. This enables the model to detect even small, flexible, floating debris in a dynamic scene. However, it makes the optimization under-constrained. To change the optimization from under-constrained to over-constrained while maintaining the model’s flexibility, ”moving object detection loss” and ”synchrony loss” are designed. The algorithm is trained in an unsupervised fashion. The primary results are in no way comparable to the current state of the art. Because the training process is so slow, it is difficult to compare it to the current state of the art. Also, the algorithm lacks stability. In addition, the optical flow model is extremely noisy and naive. At the end, some solutions are suggested to address these issues

Dense Vision in Image-guided Surgery

Image-guided surgery needs an efficient and effective camera tracking system in order to perform augmented reality for overlaying preoperative models or label cancerous tissues on the 2D video images of the surgical scene. Tracking in endoscopic/laparoscopic scenes however is an extremely difficult task primarily due to tissue deformation, instrument invasion into the surgical scene and the presence of specular highlights. State of the art feature-based SLAM systems such as PTAM fail in tracking such scenes since the number of good features to track is very limited. When the scene is smoky and when there are instrument motions, it will cause feature-based tracking to fail immediately. The work of this thesis provides a systematic approach to this problem using dense vision. We initially attempted to register a 3D preoperative model with multiple 2D endoscopic/laparoscopic images using a dense method but this approach did not perform well. We subsequently proposed stereo reconstruction to directly obtain the 3D structure of the scene. By using the dense reconstructed model together with robust estimation, we demonstrate that dense stereo tracking can be incredibly robust even within extremely challenging endoscopic/laparoscopic scenes. Several validation experiments have been conducted in this thesis. The proposed stereo reconstruction algorithm has turned out to be the state of the art method for several publicly available ground truth datasets. Furthermore, the proposed robust dense stereo tracking algorithm has been proved highly accurate in synthetic environment (< 0.1 mm RMSE) and qualitatively extremely robust when being applied to real scenes in RALP prostatectomy surgery. This is an important step toward achieving accurate image-guided laparoscopic surgery.Open Acces