Discrete Optimization Methods for Segmentation and Matching

This dissertation studies discrete optimization methods for several computer vision problems. In the first part, a new objective function for superpixel segmentation is proposed. This objective function consists of two components: entropy rate of a random walk on a graph and a balancing term. The entropy rate favors formation of compact and homogeneous clusters, while the balancing function encourages clusters with similar sizes. I present a new graph construction for images and show that this construction induces a matroid. The segmentation is then given by the graph topology which maximizes the objective function under the matroid constraint. By exploiting submodular and monotonic properties of the objective function, I develop an efficient algorithm with a worst-case performance bound of $\frac{1}{2}$ for the superpixel segmentation problem. Extensive experiments on the Berkeley segmentation benchmark show the proposed algorithm outperforms the state of the art in all the standard evaluation metrics. Next, I propose a video segmentation algorithm by maximizing a submodular objective function subject to a matroid constraint. This function is similar to the standard energy function in computer vision with unary terms, pairwise terms from the Potts model, and a novel higher-order term based on appearance histograms. I show that the standard Potts model prior, which becomes non-submodular for multi-label problems, still induces a submodular function in a maximization framework. A new higher-order prior further enforces consistency in the appearance histograms both spatially and temporally across the video. The matroid constraint leads to a simple algorithm with a performance bound of $\frac{1}{2}$. A branch and bound procedure is also presented to improve the solution computed by the algorithm. The last part of the dissertation studies the object localization problem in images given a single hand-drawn example or a gallery of shapes as the object model. Although many shape matching algorithms have been proposed for the problem, chamfer matching remains to be the preferred method when speed and robustness are considered. In this dissertation, I significantly improve the accuracy of chamfer matching while reducing the computational time from linear to sublinear (shown empirically). It is achieved by incorporating edge orientation information in the matching algorithm so the resulting cost function is piecewise smooth and the cost variation is tightly bounded. Moreover, I present a sublinear time algorithm for exact computation of the directional chamfer matching score using techniques from 3D distance transforms and directional integral images. In addition, the smooth cost function allows one to bound the cost distribution of large neighborhoods and skip the bad hypotheses. Experiments show that the proposed approach improves the speed of the original chamfer matching up to an order of 45 times, and it is much faster than many state of art techniques while the accuracy is comparable. I further demonstrate the application of the proposed algorithm in providing seamless operation for a robotic bin picking system

Automated freeform assembly of threaded fasteners

Over the past two decades, a major part of the manufacturing and assembly market has been driven by its customer requirements. Increasing customer demand for personalised products create the demand for smaller batch sizes, shorter production times, lower costs, and the flexibility to produce families of products - or different parts - with the same sets of equipment. Consequently, manufacturing companies have deployed various automation systems and production strategies to improve their resource efficiency and move towards right-first-time production. However, many of these automated systems, which are involved with robot-based, repeatable assembly automation, require component- specific fixtures for accurate positioning and extensive robot programming, to achieve flexibility in their production. Threaded fastening operations are widely used in assembly. In high-volume production, the fastening processes are commonly automated using jigs, fixtures, and semi-automated tools. This form of automation delivers reliable assembly results at the expense of flexibility and requires component variability to be adequately controlled. On the other hand, in low- volume, high- value manufacturing, fastening processes are typically carried out manually by skilled workers. This research is aimed at addressing the aforementioned issues by developing a freeform automated threaded fastener assembly system that uses 3D visual guidance. The proof-of-concept system developed focuses on picking up fasteners from clutter, identifying a hole feature in an imprecisely positioned target component and carry out torque-controlled fastening. This approach has achieved flexibility and adaptability without the use of dedicated fixtures and robot programming. This research also investigates and evaluates different 3D imaging technology to identify the suitable technology required for fastener assembly in a non-structured industrial environment. The proposed solution utilises the commercially available technologies to enhance the precision and speed of identification of components for assembly processes, thereby improving and validating the possibility of reliably implementing this solution for industrial applications. As a part of this research, a number of novel algorithms are developed to robustly identify assembly components located in a random environment by enhancing the existing methods and technologies within the domain of the fastening processes. A bolt identification algorithm was developed to identify bolts located in a random clutter by enhancing the existing surface-based matching algorithm. A novel hole feature identification algorithm was developed to detect threaded holes and identify its size and location in 3D. The developed bolt and feature identification algorithms are robust and has sub-millimetre accuracy required to perform successful fastener assembly in industrial conditions. In addition, the processing time required for these identification algorithms - to identify and localise bolts and hole features - is less than a second, thereby increasing the speed of fastener assembly