Spatially Coherent Geometric Class Labeling of Images and Its Applications

Automatic scene analysis is an active research area and is useful in many applications such as robotics and automation, industrial manufacturing, architectural design and multimedia. 3D structural information is one of the most important cues for scene analysis. In this thesis, we present a geometric labeling method to automatically extract rough 3D information from a single 2D image. Our method partitions an image scene into five geometric regions through labeling every image pixel as one of the five geometric classes (namely, “bottom”, “left ”, “center”, “right”, and “top” ). We formulate the geometric labeling problem as an energy minimization problem and optimize the energy with a graph cut based algorithm. In our energy function, we address the spatial consistency of the geometric labels in the scene while preserving discontinuities along image intensity edges. We also incorporate ordering constraints in our energy function. Ordering constraints specify the possible relative positional labels for neighbor pixels. For example, a pixel labeled as the “left” can not be the right of a pixel labeled as the “right” and a pixel labeled as the “bottom” can not be above a pixel labeled as the “top”. Ordering constraints arise naturally in a real scene. We observed that when ordering constraints are used, the commonly used graph-cut based «-expansion is more likely to get stuck in local minima. To overcome this, we developed new graph-cut moves which we call order-preserving moves. Unlike «-expansion which works for two labels in each move, order-preserving moves act on all labels. Although the global minimum is still not guaranteed, we will show that optimization with order-preserving moves is shown to perform significantly better than «-expansion. Experimental results show that it is possible to significantly increase the percentage of reasonably good labeling by promoting spatial consistency and incorporating ordering constraints. It is also shown that the order-preserving moves performs significantly better than the commonly used «-expansion when ordering constraints are used as there is a significantly improvement in computational efficiency and optimality while the improvement in accuracy of pixel labeling is also modest. in We also demonstrate the usefulness of the extracted 3D structure information of a scene in applications such as novel view generation, virtual scene walk-through, semantic segmentation, scene synthesis, and scene text extraction. We also show how we can apply this order-preserving moves for certain simple shape priors in graph-cut segmentation. Our geometric labeling method has the following main contributions: (i) We develop a new class of graph-cut moves called order-preserving moves, which performs significantly better than «-expansion when ordering constraints are used. (ii) We formulate the problem in a global optimization framework where we address the spatial consistency of labels in a scene by formulating an energy function which encourages spatial consistency between neighboring pixels while preserving discontinuities along image intensity edges. (iii) We incorporate relative ordering information about the labels in our energy function. (iv) We show that our ordering constraints can also be used in other applications such as object part segmentation. (v) We also show how the proposed order-preserving moves can be used for certain simple shape priors in graph-cut segmentation

Complexity of Discrete Energy Minimization Problems

Discrete energy minimization is widely-used in computer vision and machine learning for problems such as MAP inference in graphical models. The problem, in general, is notoriously intractable, and finding the global optimal solution is known to be NP-hard. However, is it possible to approximate this problem with a reasonable ratio bound on the solution quality in polynomial time? We show in this paper that the answer is no. Specifically, we show that general energy minimization, even in the 2-label pairwise case, and planar energy minimization with three or more labels are exp-APX-complete. This finding rules out the existence of any approximation algorithm with a sub-exponential approximation ratio in the input size for these two problems, including constant factor approximations. Moreover, we collect and review the computational complexity of several subclass problems and arrange them on a complexity scale consisting of three major complexity classes -- PO, APX, and exp-APX, corresponding to problems that are solvable, approximable, and inapproximable in polynomial time. Problems in the first two complexity classes can serve as alternative tractable formulations to the inapproximable ones. This paper can help vision researchers to select an appropriate model for an application or guide them in designing new algorithms.Comment: ECCV'16 accepte

An improved Ant Colony System for the Sequential Ordering Problem

It is not rare that the performance of one metaheuristic algorithm can be improved by incorporating ideas taken from another. In this article we present how Simulated Annealing (SA) can be used to improve the efficiency of the Ant Colony System (ACS) and Enhanced ACS when solving the Sequential Ordering Problem (SOP). Moreover, we show how the very same ideas can be applied to improve the convergence of a dedicated local search, i.e. the SOP-3-exchange algorithm. A statistical analysis of the proposed algorithms both in terms of finding suitable parameter values and the quality of the generated solutions is presented based on a series of computational experiments conducted on SOP instances from the well-known TSPLIB and SOPLIB2006 repositories. The proposed ACS-SA and EACS-SA algorithms often generate solutions of better quality than the ACS and EACS, respectively. Moreover, the EACS-SA algorithm combined with the proposed SOP-3-exchange-SA local search was able to find 10 new best solutions for the SOP instances from the SOPLIB2006 repository, thus improving the state-of-the-art results as known from the literature. Overall, the best known or improved solutions were found in 41 out of 48 cases.Comment: 30 pages, 8 tables, 11 figure

Size reduction of complex networks preserving modularity

The ubiquity of modular structure in real-world complex networks is being the focus of attention in many trials to understand the interplay between network topology and functionality. The best approaches to the identification of modular structure are based on the optimization of a quality function known as modularity. However this optimization is a hard task provided that the computational complexity of the problem is in the NP-hard class. Here we propose an exact method for reducing the size of weighted (directed and undirected) complex networks while maintaining invariant its modularity. This size reduction allows the heuristic algorithms that optimize modularity for a better exploration of the modularity landscape. We compare the modularity obtained in several real complex-networks by using the Extremal Optimization algorithm, before and after the size reduction, showing the improvement obtained. We speculate that the proposed analytical size reduction could be extended to an exact coarse graining of the network in the scope of real-space renormalization.Comment: 14 pages, 2 figure

Towards Zero-Waste Furniture Design

In traditional design, shapes are first conceived, and then fabricated. While this decoupling simplifies the design process, it can result in inefficient material usage, especially where off-cut pieces are hard to reuse. The designer, in absence of explicit feedback on material usage remains helpless to effectively adapt the design -- even though design variabilities exist. In this paper, we investigate {\em waste minimizing furniture design} wherein based on the current design, the user is presented with design variations that result in more effective usage of materials. Technically, we dynamically analyze material space layout to determine {\em which} parts to change and {\em how}, while maintaining original design intent specified in the form of design constraints. We evaluate the approach on simple and complex furniture design scenarios, and demonstrate effective material usage that is difficult, if not impossible, to achieve without computational support

High-Quality Shared-Memory Graph Partitioning

Partitioning graphs into blocks of roughly equal size such that few edges run between blocks is a frequently needed operation in processing graphs. Recently, size, variety, and structural complexity of these networks has grown dramatically. Unfortunately, previous approaches to parallel graph partitioning have problems in this context since they often show a negative trade-off between speed and quality. We present an approach to multi-level shared-memory parallel graph partitioning that guarantees balanced solutions, shows high speed-ups for a variety of large graphs and yields very good quality independently of the number of cores used. For example, on 31 cores, our algorithm partitions our largest test instance into 16 blocks cutting less than half the number of edges than our main competitor when both algorithms are given the same amount of time. Important ingredients include parallel label propagation for both coarsening and improvement, parallel initial partitioning, a simple yet effective approach to parallel localized local search, and fast locality preserving hash tables