Partial Matching Problem Research Articles

A Robust Framework for One-Shot Key Information Extraction via Deep Partial Graph Matching.

Text field labelling plays a key role in Key Information Extraction (KIE) from structured document images. However, existing methods ignore the field drift and outlier problems, which limit their performance and make them less robust. This paper casts the text field labelling problem into a partial graph matching problem and proposes an end-to-end trainable framework called Deep Partial Graph Matching (dPGM) for the one-shot KIE task. It represents each document as a graph and estimates the correspondence between text fields from different documents by maximizing the graph similarity of different documents. Our framework obtains a strict one-to-one correspondence by adopting a combinatorial solver module with an extra one-to-(at most)-one mapping constraint to do the exact graph matching, which leads to the robustness of the field drift problem and the outlier problem. Finally, a large one-shot KIE dataset named DKIE is collected and annotated to promote research of the KIE task. This dataset will be released to the research and industry communities. Extensive experiments on both the public and our new DKIE datasets show that our method can achieve state-of-the-art performance and is more robust than existing methods.

Universe Points Representation Learning for Partial Multi-Graph Matching

Many challenges from natural world can be formulated as a graph matching problem. Previous deep learning-based methods mainly consider a full two-graph matching setting. In this work, we study the more general partial matching problem with multi-graph cycle consistency guarantees. Building on a recent progress in deep learning on graphs, we propose a novel data-driven method (URL) for partial multi-graph matching, which uses an object-to-universe formulation and learns latent representations of abstract universe points. The proposed approach advances the state of the art in semantic keypoint matching problem, evaluated on Pascal VOC, CUB, and Willow datasets. Moreover, the set of controlled experiments on a synthetic graph matching dataset demonstrates the scalability of our method to graphs with large number of nodes and its robustness to high partiality.

CORE

Complex Event Recognition (CER) systems are a prominent technology for finding user-defined query patterns over large data streams in real time. CER query evaluation is known to be computationally challenging, since it requires maintaining a set of partial matches, and this set quickly grows super-linearly in the number of processed events. We present CORE, a novel COmplex event Recognition Engine that focuses on the efficient evaluation of a large class of complex event queries, including time windows as well as the partition-by event correlation operator. This engine uses a novel automaton-based evaluation algorithm that circumvents the super-linear partial match problem: under data complexity, it takes constant time per input event to maintain a data structure that compactly represents the set of partial matches and, once a match is found, the query results may be enumerated from the data structure with output-linear delay. We experimentally compare CORE against state-of-the-art CER systems on real-world data. We show that (1) CORE's performance is stable with respect to both query and time window size, and (2) CORE outperforms the other systems by up to five orders of magnitude on different workloads.

Parameter-Free Ordered Partial Match Alignment with Hidden State Time Warping

This paper investigates an ordered partial matching alignment problem, in which the goal is to align two sequences in the presence of potentially non-matching regions. We propose a novel parameter-free dynamic programming alignment method called hidden state time warping that allows an alignment path to switch between two different planes: a “visible” plane corresponding to matching sections and a “hidden” plane corresponding to non-matching sections. By defining two distinct planes, we can allow different types of time warping in each plane (e.g., imposing a maximum warping factor in matching regions while allowing completely unconstrained movements in non-matching regions). The resulting algorithm can determine the optimal continuous alignment path via dynamic programming, and the visible plane induces a (possibly) discontinuous alignment path containing matching regions. We show that this approach outperforms existing parameter-free methods on two different partial matching alignment problems involving speech and music.

A parametric analysis of discrete Hamiltonian functional maps

AbstractIn this paper we develop an in‐depth theoretical investigation of the discrete Hamiltonian eigenbasis, which remains quite unexplored in the geometry processing community. This choice is supported by the fact that Dirichlet eigenfunctions can be equivalently computed by defining a Hamiltonian operator, whose potential energy and localization region can be controlled with ease. We vary with continuity the potential energy and study the relationship between the Dirichlet Laplacian and the Hamiltonian eigenbases with the functional map formalism. We develop a global analysis to capture the asymptotic behavior of the eigenpairs. We then focus on their local interactions, namely the veering patterns that arise between proximal eigenvalues. Armed with this knowledge, we are able to track the eigenfunctions in all possible configurations, shedding light on the nature of the functional maps. We exploit the Hamiltonian‐Dirichlet connection in a partial shape matching problem, obtaining state of the art results, and provide directions where our theoretical findings could be applied in future research.

Partial Discharge Data Matching Method for GIS Case-Based Reasoning

With the accumulation of partial discharge (PD) detection data from substation, case-based reasoning (CBR), which computes the match degree between detected PD data and historical case data provides new ideas for the interpretation and evaluation of partial discharge data. Aiming at the problem of partial discharge data matching, this paper proposes a data matching method based on a variational autoencoder (VAE). A VAE network model for partial discharge data is constructed to extract the deep eigenvalues. Cosine distance is then used to calculate the match degree between different partial discharge data. To verify the advantages of the proposed method, a partial discharge dataset was established through a partial discharge experiment and live detections on substation site. The proposed method was compared with other feature extraction methods and matching methods including statistical features, deep belief networks (DBN), deep convolutional neural networks (CNN), Euclidean distances, and correlation coefficients. The experimental results show that the cosine distance match degree based on the VAE feature vector can effectively detect similar partial discharge data compared with other data matching methods.

Isometric 3D Shape Partial Matching Using GD-DNA

Isometric 3D shape partial matching has attracted a great amount of interest, with a plethora of applications ranging from shape recognition to texture mapping. In this paper, we propose a novel isometric 3D shape partial matching algorithm using the geodesic disk Laplace spectrum (GD-DNA). It transforms the partial matching problem into the geodesic disk matching problem. Firstly, the largest enclosed geodesic disk extracted from the partial shape is matched with geodesic disks from the full shape by the Laplace spectrum of the geodesic disk. Secondly, Generalized Multi-Dimensional Scaling algorithm (GMDS) and Euclidean embedding are conducted to establish final point correspondences between the partial and the full shape using the matched geodesic disk pair. The proposed GD-DNA is discriminative for matching geodesic disks, and it can well solve the anchor point selection problem in challenging partial shape matching tasks. Experimental results on the Shape Retrieval Contest 2016 (SHREC’16) benchmark validate the proposed method, and comparisons with isometric partial matching algorithms in the literature show that our method has a higher precision.

Classifying fragments of terracotta warriors using template-based partial matching

Large numbers of Terracotta Warriors fragments are mixed up when they are excavated, which calls the need for classifying them in order to avoid one to all matches and improve the efficiency of reassembly. In this paper, we propose a novel template-based classification algorithm for Terracotta Warriors fragments, which transforms the problem of classification into the problem of partial shape matching. Firstly, a few distinct regions, which indicate categories of the fragments, are selected as templates from collections of fragments. Secondly, a novel partial matching procedure is proposed to find whether a fragment have a sub-region that is similar to one of the templates. If there exists a sub-region on the fragment that is similar to one of the templates, this fragment is considered to belong to the category that the matching template represents. The partial matching procedure consists of a coarse matching and a fine matching, which utilizes the normal distribution descriptor and the modified point feature histogram descriptor, respectively. The normal distribution descriptor characterizes the structure of a Euclidean-sphere region and the modified point feature histogram descriptor characterizes the structure of a geodesic-disk region. Experiments have been conducted on Terracotta Warriors fragments that are scanned from real sites to verify the effectiveness of our method. Comparing with other partial matching methods, more accurate classification results are achieved.

Stable Matching Games: Manipulation via Subgraph Isomorphism

In this paper we consider a problem that arises from a strategic issue in the stable matching model (with complete preference lists) from the viewpoint of exact-exponential time algorithms. Specifically, we study the Stable Extension of Partial Matching (SEOPM) problem, where the input consists of the complete preference lists of men, and a partial matching. The objective is to find (if one exists) a set of preference lists of women, such that the men-optimal Gale–Shapley algorithm outputs a perfect matching that contains the given partial matching. Kobayashi and Matsui (Algorithmica 58:151–169, 2010) proved this problem is NP-complete. In this article, we give an exact-exponential algorithm for SEOPM running in time $$2^{{\mathcal {O}} (n)}$$ , where n denotes the number of men/women. We complement our algorithmic finding by showing that unless Exponential Time Hypothesis (ETH) fails, our algorithm is asymptotically optimal. That is, unless ETH fails, there is no algorithm for SEOPM running in time $$2^{o(n)}$$ . Our algorithm is a non-trivial combination of a parameterized algorithm for Subgraph Isomorphism, a relationship between stable matching and finding an out-branching in an appropriate graph and enumerating all possible non-isomorphic out-branchings. Our results cover both the cases when the preference lists are strict and complete, and when they are strict but possibly incomplete.

A novel method for 2D nonrigid partial shape matching

Abstract There are two categories of partial shape matching problem: whole-to-part matching and part-to-part matching. The first establishes the best match between an open curve and a part of a closed curve, while the second is to find a part of the first input closed curve that can be well aligned with a part of the second input closed curve. In this paper, we present a novel approach to solve these two categories of the partial shape matching problem. First, we propose a novel shape descriptor, triangular centroid distances (TCDs), for shape representation; the TCDs shape descriptor is invariant to translation, rotation, scaling, and considerable shape deformations. Then, using the TCDs shape descriptor, we present a method to deal with the whole-to-part partial shape matching problem. Finally, we extend our work to part-to-part partial shape matching. Here, we propose a new approach, again using the TCDs shape descriptor, to solve the part-to-part partial shape matching problem. Experimental results demonstrate that our method outperforms existing methods in 2D nonrigid partial shape matching.

Sketch-based image retrieval using hierarchical partial matching

In sketch-based image retrieval (SBIR) systems, representing photo-realistic images by their strong edges is an intuitive and effective way to bridge the appearance gap between sketches and photo-realistic images. However, noisy edges and missing edges usually enlarge the appearance gap and significantly degrade retrieval performance. To alleviate the impact, we formalize the matching task between the sketches and extracted edges of photo-realistic images as a partial matching problem. We treat the sketches and extracted edges as a set of line segments which serve as the basis for better shape description and partial matching. We propose a new descriptor, structure point, to represent sketches and the extracted edges. Based on the structure point, a decompose-and-assemble hierarchical matching algorithm is developed to match sketches and extracted edges. Observing that false matches can degrade performance, we introduce a spatial constraint to filter the false matches. We have tested the proposed framework on public datasets and a new dataset of three million images which we recently collected for the SBIR evaluation purpose. We compared our method with the state-of-the-art methods (SHoG and GF-HOG). The experimental results show that our framework significantly improves retrieval performance.

Bin Ratio-Based Histogram Distances and Their Application to Image Classification.

Large variations in image background may cause partial matching and normalization problems for histogram-based representations, i.e., the histograms of the same category may have bins which are significantly different, and normalization may produce large changes in the differences between corresponding bins. In this paper, we deal with this problem by using the ratios between bin values of histograms, rather than bin values' differences which are used in the traditional histogram distances. We propose a bin ratio-based histogram distance (BRD), which is an intra-cross-bin distance, in contrast with previous bin-to-bin distances and cross-bin distances. The BRD is robust to partial matching and histogram normalization, and captures correlations between bins with only a linear computational complexity. We combine the BRD with the ℓ1 histogram distance and the χ(2) histogram distance to generate the ℓ1 BRD and the χ(2) BRD, respectively. These combinations exploit and benefit from the robustness of the BRD under partial matching and the robustness of the ℓ1 and χ(2) distances to small noise. We propose a method for assessing the robustness of histogram distances to partial matching. The BRDs and logistic regression-based histogram fusion are applied to image classification. The experimental results on synthetic data sets show the robustness of the BRDs to partial matching, and the experiments on seven benchmark data sets demonstrate promising results of the BRDs for image classification.

Subimage sensitive eigenvalue spectra for image comparison

This publication is a contribution to basic research in image comparison using eigenvalue spectra as features. The differential-geometric approach of eigenvalue spectrum-based descriptors is naturally applicable to shape data, but so far little work has been done to transfer it to the setting of image data painted on a rectangle or general curved surface. We present a new semi-global feature descriptor that also contains information about geometry of shapes visible in the image. This may not only improve the performance of the resulting distance measures, but may even enable us to approach the partial matching problem using eigenvalue spectra, which were previously only considered as global feature descriptors. We introduce some concepts that are useful in designing and understanding the behaviour of similar fingerprinting algorithms for images (and surfaces) and discuss some preliminary results.

GNCCP-Graduated NonConvexityand Concavity Procedure.

In this paper we propose the graduated nonconvexity and concavity procedure (GNCCP) as a general optimization framework to approximately solve the combinatorial optimization problems defined on the set of partial permutation matrices. GNCCP comprises two sub-procedures, graduated nonconvexity which realizes a convex relaxation and graduated concavity which realizes a concave relaxation. It is proved that GNCCP realizes exactly a type of convex-concave relaxation procedure (CCRP), but with a much simpler formulation without needing convex or concave relaxation in an explicit way. Actually, GNCCP involves only the gradient of the objective function and is therefore very easy to use in practical applications. Two typical related NP-hard problems, partial graph matching and quadratic assignment problem (QAP), are employed to demonstrate its simplicity and state-of-the-art performance.

3D object retrieval via range image queries in a bag-of-visual-words context

3D object retrieval based on range image queries that represent partial views of real 3D objects is presented. The complete 3D models of the database are described by a set of panoramic views, and a Bag-of-Visual-Words model is built using SIFT features extracted from them. To address the problem of partial matching, we suggest a histogram computation scheme, on the panoramic views, that represents local information by taking into account spatial context. Furthermore, a number of optimization techniques are applied throughout the process for enhancing the retrieval performance. Its superior performance is shown by evaluating it against state-of-the-art methods on standard datasets.

Scale invariant and deformation tolerant partial shape matching

We present a novel approach to the problem of establishing the best match between an open contour and a part of a closed contour. At the heart of the proposed scheme lies a novel shape descriptor that also permits the quantification of local scale. Shape descriptors are computed along open or closed contours in a spatially non-uniform manner. The resulting ordered collections of shape descriptors constitute the global shape representation. A variant of an existing Dynamic Time Warping (DTW) matching technique is proposed to handle the matching of shape representations. Due to the properties of the employed shape descriptor, sampling scheme and matching procedure, the proposed approach performs partial shape matching that is invariant to Euclidean transformations, starting point as well as to considerable shape deformations. Additionally, the problem of matching closed-to-closed contours is naturally treated as a special case. Extensive experiments on benchmark datasets but also in the context of specific applications, demonstrate that the proposed scheme outperforms existing methods for the problem of partial shape matching and performs comparably to methods for full shape matching.

Cell-Probe Proofs

We study the nondeterministic cell-probe complexity of static data structures. We introduce cell-probe proofs (CPP), a proof system for the cell-probe model, which describes verification instead of computation in the cell-probe model. We present a combinatorial characterization of CPP. With this novel tool, we prove the following lower bounds for the nondeterministic cell-probe complexity of static data structures. –There exists a data structure problem with high nondeterministic cell-probe complexity. –For the exact nearest neighbor search (NNS) problem or the partial match problem in high dimensional Hamming space, for any data structure with Poly( n ) cells, each of which contains O ( n C ) bits where C < 1, the nondeterministic cell-probe complexity is at least Ω(log( d /log n )), where d is the dimension and n is the number of points in the data set. –For the polynomial evaluation problem of d -degree polynomial over finite field of size 2 k where d ≤ 2 k , for any data structure with s cells, each of which contains b bits, the nondeterministic cell-probe complexity is at least min (( k / b ( d − 1)), ( k −log( d −1)/log s )).

Global Correspondence Optimization for Non‐Rigid Registration of Depth Scans

AbstractWe present a registration algorithm for pairs of deforming and partial range scans that addresses the challenges of non‐rigid registration within a single non‐linear optimization. Our algorithm simultaneously solves for correspondences between points on source and target scans, confidence weights that measure the reliability of each correspondence and identify non‐overlapping areas, and a warping field that brings the source scan into alignment with the target geometry. The optimization maximizes the region of overlap and the spatial coherence of the deformation while minimizing registration error. All optimization parameters are chosen automatically; hand‐tuning is not necessary. Our method is not restricted to part‐in‐whole matching, but addresses the general problem of partial matching, and requires no explicit prior correspondences or feature points. We evaluate the performance and robustness of our method using scan data acquired by a structured light scanner and compare our method with existing non‐rigid registration algorithms.

A Framework for Handling Spatiotemporal Variations in Video Copy Detection

An effective video copy detection framework should be robust against spatial and temporal variations, e.g., changes in brightness and speed. To this end, a content-based approach for video copy detection is proposed. We define the problem as a partial matching problem in a probabilistic model and transform it into a shortest-path problem in a matching graph. To reduce the computation costs of the proposed framework, we introduce some methods that rapidly select key frames and candidate segments from a large amount of video data. The experiment results show that the proposed approach not only handles spatial and temporal variations well, but it also reduces the computation costs substantially.

An elastic partial shape matching technique

We consider the problem of partial shape matching. We propose to transform shapes into sequences and utilize an algorithm that determines a subsequence of a target sequence that best matches a query. In the proposed algorithm we map the problem of the best matching subsequence to the problem of a cheapest path in a directed acyclic graph (DAG). The approach allows us to compute the optimal scale and translation of sequence values, which is a nontrivial problem in the case of subsequence matching. Our experimental results demonstrate that the proposed algorithm outperforms the commonly used techniques in retrieval accuracy.