Fast connected component labeling algorithm: a non voxel-based approach

This paper presents a new approach to achieve connected component labeling on both binary images and volumes by using the Extreme Vertices Model (EVM), a representation model for orthogonal polyhedra, applied to digital images and volume datasets recently. In contrast with previous techniques, this method does not use a voxel-based approach but deals with the inner sections of the object.Postprint (published version

Using topological sweep to extract the boundaries of regions in maps represented by region quadtrees

A variant of the plane sweep paradigm known as topological sweep is adapted to solve geometric problems involving two-dimensional regions when the underlying representation is a region quadtree. The utility of this technique is illustrated by showing how it can be used to extract the boundaries of a map in O(M) space and O(Ma(M)) time, where M is the number of quad tree blocks in the map, and a(·) is the (extremely slowly growing) inverse of Ackerman's function. The algorithm works for maps that contain multiple regions as well as holes. The algorithm makes use of active objects (in the form of regions) and an active border. It keeps track of the current position in the active border so that at each step no search is necessary. The algorithm represents a considerable improvement over a previous approach whose worst-case execution time is proportional to the product of the number of blocks in the map and the resolution of the quad tree (i.e., the maximum level of decomposition). The algorithm works for many different quadtree representations including those where the quadtree is stored in external storage

The Connected Component Algorithm on The NON-VON Supercomputer

The NON-VON Supercomputer is a highly parallel tree-structured computer that is being Implemented at Columbia University. In this paper, we demonstrate that tree architectures with their favorable characteristics for VLSI Implementation, and fast global broadcast, lend themselves easily and naturally to the representation and manipulation of Images represented by hierarchical data structures A description of NON-VON architecture IS presented With an emphasis on the special architectural features that will be used m our Image understanding algorithms. We adopt a variation of the quad tree data structure, called the binary Image tree, to represent images in the NON-VON tree We show how Images are loaded in the NON-VON tree, and present the algorithm for budding the binary Image trees. An efficient Implementation of the connected component labeling algorithm on NON-VON is then presented Simulation results are discussed, and we show the fast execution time of the algorithm on NON-VON. Other algorithms are also developed, such as hlstogrammlng, Hough transform, Set operations and Image correlation, and we can conclude that NON-VON can be used to Implement efficiently several :important Image understanding task

Self-adapting structuring and representation of space

The objective of this report is to propose a syntactic formalism for space representation. Beside the well known advantages of hierarchical data structure, the underlying approach has the additional strength of self-adapting to a spatial structure at hand. The formalism is called puzzletree because its generation results in a number of blocks which in a certain order -- like a puzzle - reconstruct the original space. The strength of the approach does not lie only in providing a compact representation of space (e.g. high compression), but also in attaining an ideal basis for further knowledge-based modeling and recognition of objects. The approach may be applied to any higher-dimensioned space (e.g. images, volumes). The report concentrates on the principles of puzzletrees by explaining the underlying heuristic for their generation with respect to 2D spaces, i.e. images, but also schemes their application to volume data. Furthermore, the paper outlines the use of puzzletrees to facilitate higher-level operations like image segmentation or object recognition. Finally, results are shown and a comparison to conventional region quadtrees is done

Image Understanding Algorithms on Fine-Grained Tree-Structured SIMD Machines

An Important goal for researchers In computer vision is the construction vision systems that Interpret Image data in real time. Such systems typically require a large amount of computation for processing raw Image data at the lowest level, and for sophisticated decision making at the highest level Recent advances In VLSI circuitry· have led to several proposals for parallel architectures for computer vision systems. In this theSIS. we demonstrate that fine-grained tree-structured SIMD machines, which have favorable characteristics for efficient VLSI Implementation, can be used for the rapid execution of a wide range of Image understanding tasks We also Identify the limitations of these architectures and propose methods to ameliorate these difficulties. The NON-VON supercomputer, currently being constructed at Columbia University, is an example of such an architecture. The major contribution of this thesis IS the development and analysis of several parallel Image understanding algorithms for the class of architectures under consideration The algorithms developed In this research have been selected to span different levels of computer vision tasks They Include Image correlation, hlstogrammlng, connected component labeling, the computation of geometric properties, set operations, the Hough transform method for detecting object boundaries, and the correspondence problem In moving light display applications. The algorithms Incorporate novel approaches to reduce the effects of communication bottleneck usually associated With tree architecture

The dual tree of a recursive triangulation of the disk

In the recursive lamination of the disk, one tries to add chords one after another at random; a chord is kept and inserted if it does not intersect any of the previously inserted ones. Curien and Le Gall [Ann. Probab. 39 (2011) 2224-2270] have proved that the set of chords converges to a limit triangulation of the disk encoded by a continuous process $\mathscr{M}$. Based on a new approach resembling ideas from the so-called contraction method in function spaces, we prove that, when properly rescaled, the planar dual of the discrete lamination converges almost surely in the Gromov-Hausdorff sense to a limit real tree $\mathscr{T}$, which is encoded by $\mathscr{M}$. This confirms a conjecture of Curien and Le Gall.Comment: Published in at http://dx.doi.org/10.1214/13-AOP894 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

Probabilistic and Deep Learning Algorithms for the Analysis of Imagery Data

Accurate object classification is a challenging problem for various low to high resolution imagery data. This applies to both natural as well as synthetic image datasets. However, each object recognition dataset poses its own distinct set of domain-specific problems. In order to address these issues, we need to devise intelligent learning algorithms which require a deep understanding and careful analysis of the feature space. In this thesis, we introduce three new learning frameworks for the analysis of both airborne images (NAIP dataset) and handwritten digit datasets without and with noise (MNIST and n-MNIST respectively). First, we propose a probabilistic framework for the analysis of the NAIP dataset which includes (1) an unsupervised segmentation module based on the Statistical Region Merging algorithm, (2) a feature extraction module that extracts a set of standard hand-crafted texture features from the images, (3) a supervised classification algorithm based on Feedforward Backpropagation Neural Networks, and (4) a structured prediction framework using Conditional Random Fields that integrates the results of the segmentation and classification modules into a single composite model to generate the final class labels. Next, we introduce two new datasets SAT-4 and SAT-6 sampled from the NAIP imagery and use them to evaluate a multitude of Deep Learning algorithms including Deep Belief Networks (DBN), Convolutional Neural Networks (CNN) and Stacked Autoencoders (SAE) for generating class labels. Finally, we propose a learning framework by integrating hand-crafted texture features with a DBN. A DBN uses an unsupervised pre-training phase to perform initialization of the parameters of a Feedforward Backpropagation Neural Network to a global error basin which can then be improved using a round of supervised fine-tuning using Feedforward Backpropagation Neural Networks. These networks can subsequently be used for classification. In the following discussion, we show that the integration of hand-crafted features with DBN shows significant improvement in performance as compared to traditional DBN models which take raw image pixels as input. We also investigate why this integration proves to be particularly useful for aerial datasets using a statistical analysis based on Distribution Separability Criterion. Then we introduce a new dataset called noisy-MNIST (n-MNIST) by adding (1) additive white gaussian noise (AWGN), (2) motion blur and (3) Reduced contrast and AWGN to the MNIST dataset and present a learning algorithm by combining probabilistic quadtrees and Deep Belief Networks. This dynamic integration of the Deep Belief Network with the probabilistic quadtrees provide significant improvement over traditional DBN models on both the MNIST and the n-MNIST datasets. Finally, we extend our experiments on aerial imagery to the class of general texture images and present a theoretical analysis of Deep Neural Networks applied to texture classification. We derive the size of the feature space of textural features and also derive the Vapnik-Chervonenkis dimension of certain classes of Neural Networks. We also derive some useful results on intrinsic dimension and relative contrast of texture datasets and use these to highlight the differences between texture datasets and general object recognition datasets

Representing Images Using the Quadtree Data Structure (Hebrew Consonants and Vowels)

Computing and Information Science