The PSEIKI Report—Version 2. Evidence Accumulation and Flow of Control in a Hierarchical Spatial Reasoning System

A fundamental goal of computer vision is the development of systems capable of carrying out scene interpretation while taking into account all the available knowledge. In this report, we have focused on how the interpretation task may be aided by expected-scene information which, in most cases, would not be in registration with the perceived scene. In this report, we describe PSEIKI, a framework for expectation-driven interpretation of image data. PSEIKI builds abstraction hierarchies in image data using, for cues, supplied abstraction hierarchies in a scene expectation map. Hypothesized abstractions in the image data are geometrically compared with the known abstractions in the expected scene; the metrics used for these comparisons translate into belief values. The Dempster-Shafer formalism is used to accumulate beliefs for the synthesized abstractions in the image data. For accumulating belief values, a computationally efficient variation of Dempster’s rule of combination is developed to enable the system to deal with the overwhelming amount of information present in most images. This variation of Dempster’s rule allows the reasoning process to be embedded into the abstraction hierarchy by allowing for the propagation of belief values between elements at different levels of abstraction. The system has been implemented as a 2- panel, 5-level blackboard in OPS 83. This report also discusses the control aspects of the blackboard, achieved via a distributed monitor using the OPS83 demons and a scheduler. Various knowledge sources for forming groupings in the image data and for labeling such groupings with abstractions from the scene expectation map are also discussed

Learning Ultrametric Trees for Optimal Transport Regression

Optimal transport provides a metric which quantifies the dissimilarity between probability measures. For measures supported in discrete metric spaces, finding the optimal transport distance has cubic time complexity in the size of the space. However, measures supported on trees admit a closed-form optimal transport that can be computed in linear time. In this paper, we aim to find an optimal tree structure for a given discrete metric space so that the tree-Wasserstein distance approximates the optimal transport distance in the original space. One of our key ideas is to cast the problem in ultrametric spaces. This helps us optimize over the space of ultrametric trees -- a mixed-discrete and continuous optimization problem -- via projected gradient decent over the space of ultrametric matrices. During optimization, we project the parameters to the ultrametric space via a hierarchical minimum spanning tree algorithm, equivalent to the closest projection to ultrametrics under the supremum norm. Experimental results on real datasets show that our approach outperforms previous approaches (e.g. Flowtree, Quadtree) in approximating optimal transport distances. Finally, experiments on synthetic data generated on ground truth trees show that our algorithm can accurately uncover the underlying trees

Image Understanding by Hierarchical Symbolic Representation and Inexact Matching of Attributed Graphs

We study the symbolic representation of imagery information by a powerful global representation scheme in the form of Attributed Relational Graph (ARG), and propose new techniques for the extraction of such representation from spatial-domain images, and for performing the task of image understanding through the analysis of the extracted ARG representation. To achieve practical image understanding tasks, the system needs to comprehend the imagery information in a global form. Therefore, we propose a multi-layer hierarchical scheme for the extraction of global symbolic representation from spatial-domain images. The proposed scheme produces a symbolic mapping of the input data in terms of an output alphabet, whose elements are defined over global subimages. The proposed scheme uses a combination of model-driven and data-driven concepts. The model- driven principle is represented by a graph transducer, which is used to specify the alphabet at each layer in the scheme. A symbolic mapping is driven by the input data to map the input local alphabet into the output global alphabet. Through the iterative application of the symbolic transformational mapping at different levels of hierarchy, the system extracts a global representation from the image in the form of attributed relational graphs. Further processing and interpretation of the imagery information can, then, be performed on their ARG representation. We also propose an efficient approach for calculating a distance measure and finding the best inexact matching configuration between attributed relational graphs. For two ARGs, we define sequences of weighted error-transformations which when performed on one ARG (or a subgraph of it), will produce the other ARG. A distance measure between two ARGs is defined as the weight of the sequence which possesses minimum total-weight. Moreover, this minimum-total weight sequence defines the best inexact matching configuration between the two ARGs. The global minimization over the possible sequences is performed by a dynamic programming technique, the approach shows good results for ARGs of practical sizes. The proposed system possesses the capability to inference the alphabets of the ARG representation which it uses. In the inference phase, the hierarchical scheme is usually driven by the input data only, which normally consist of images of model objects. It extracts the global alphabet of the ARG representation of the models. The extracted model representation is then used in the operation phase of the system to: perform the mapping in the multi-layer scheme. We present our experimental results for utilizing the proposed system for locating objects in complex scenes

Invariant Spectral Hashing of Image Saliency Graph

Image hashing is the process of associating a short vector of bits to an image. The resulting summaries are useful in many applications including image indexing, image authentication and pattern recognition. These hashes need to be invariant under transformations of the image that result in similar visual content, but should drastically differ for conceptually distinct contents. This paper proposes an image hashing method that is invariant under rotation, scaling and translation of the image. The gist of our approach relies on the geometric characterization of salient point distribution in the image. This is achieved by the definition of a saliency graph connecting these points jointly with an image intensity function on the graph nodes. An invariant hash is then obtained by considering the spectrum of this function in the eigenvector basis of the graph Laplacian, that is, its graph Fourier transform. Interestingly, this spectrum is invariant under any relabeling of the graph nodes. The graph reveals geometric information of the image, making the hash robust to image transformation, yet distinct for different visual content. The efficiency of the proposed method is assessed on a set of MRI 2-D slices and on a database of faces

Book of Abstracts of the Sixth SIAM Workshop on Combinatorial Scientific Computing

Book of Abstracts of CSC14 edited by Bora UçarInternational audienceThe Sixth SIAM Workshop on Combinatorial Scientific Computing, CSC14, was organized at the Ecole Normale Supérieure de Lyon, France on 21st to 23rd July, 2014. This two and a half day event marked the sixth in a series that started ten years ago in San Francisco, USA. The CSC14 Workshop's focus was on combinatorial mathematics and algorithms in high performance computing, broadly interpreted. The workshop featured three invited talks, 27 contributed talks and eight poster presentations. All three invited talks were focused on two interesting fields of research specifically: randomized algorithms for numerical linear algebra and network analysis. The contributed talks and the posters targeted modeling, analysis, bisection, clustering, and partitioning of graphs, applied in the context of networks, sparse matrix factorizations, iterative solvers, fast multi-pole methods, automatic differentiation, high-performance computing, and linear programming. The workshop was held at the premises of the LIP laboratory of ENS Lyon and was generously supported by the LABEX MILYON (ANR-10-LABX-0070, Université de Lyon, within the program ''Investissements d'Avenir'' ANR-11-IDEX-0007 operated by the French National Research Agency), and by SIAM

Speeding-up graph-based keyword spotting in historical handwritten documents

The present paper is concerned with a graph-based system for Keyword Spotting (KWS) in historical documents. This particular system operates on segmented words that are in turn represented as graphs. The basic KWS process employs the cubic-time bipartite matching algorithm (BP). Yet, even though this graph matching procedure is relatively efficient, the computation time is a limiting factor for processing large volumes of historical manuscripts. In order to speed up our framework, we propose a novel fast rejection heuristic. This heuristic compares the node distribution of the query graph and the document graph in a polar coordinate system. This comparison can be accomplished in linear time. If the node distributions are similar enough, the BP matching is actually carried out (otherwise the document graph is rejected). In an experimental evaluation on two benchmark datasets we show that about 50% or more of the matchings can be omitted with this procedure while the KWS accuracy is not negatively affected.International Workshop on Graph-Based Representations in Pattern Recognition. GbRPR 2017: Graph-Based Representations in Pattern Recognition pp. 83-93.http://link.springer.combookseries/5582018-05-10hj2017Informatic

Keyword spotting in historical handwritten documents based on graph matching

In the last decades historical handwritten documents have become increasingly available in digital form. Yet, the accessibility to these documents with respect to browsing and searching remained limited as full automatic transcription is often not possible or not sufficiently accurate. This paper proposes a novel reliable approach for template-based keyword spotting in historical handwritten documents. In particular, our framework makes use of different graph representations for segmented word images and a sophisticated matching procedure. Moreover, we extend our method to a spotting ensemble. In an exhaustive experimental evaluation on four widely used benchmark datasets we show that the proposed approach is able to keep up or even outperform several state-of-the-art methods for template- and learning-based keyword spotting.The Hasler Foundation Switzerlandhttp://www.elsevier.com/locate/patcog2019-09-01hj2018Informatic

Incremental Construction of Generalized Voronoi Diagrams on Pointerless Quadtrees

In robotics, Generalized Voronoi Diagrams (GVDs) are widely used by mobile robots to represent the spatial topologies of their surrounding area. In this paper we consider the problem of constructing GVDs on discrete environments. Several algorithms that solve this problem exist in the literature, notably the Brushfire algorithm and its improved versions which possess local repair mechanism. However, when the area to be processed is very large or is of high resolution, the size of the metric matrices used by these algorithms to compute GVDs can be prohibitive. To address this issue, we propose an improvement on the current algorithms, using pointerless quadtrees in place of metric matrices to compute and maintain GVDs. Beyond the construction and reconstruction of a GVD, our algorithm further provides a method to approximate roadmaps in multiple granularities from the quadtree based GVD. Simulation tests in representative scenarios demonstrate that, compared with the current algorithms, our algorithm generally makes an order of magnitude improvement regarding memory cost when the area is larger than 210×210. We also demonstrate the usefulness of the approximated roadmaps for coarse-to-fine pathfinding tasks