Showing papers on "Affine transformation published in 2006"
TL;DR: This paper provides a new proof of the characterization of Riemannian centers of mass and an original gradient descent algorithm to efficiently compute them and develops the notions of mean value and covariance matrix of a random element, normal law, Mahalanobis distance and χ2 law.
Abstract: In medical image analysis and high level computer vision, there is an intensive use of geometric features like orientations, lines, and geometric transformations ranging from simple ones (orientations, lines, rigid body or affine transformations, etc.) to very complex ones like curves, surfaces, or general diffeomorphic transformations. The measurement of such geometric primitives is generally noisy in real applications and we need to use statistics either to reduce the uncertainty (estimation), to compare observations, or to test hypotheses. Unfortunately, even simple geometric primitives often belong to manifolds that are not vector spaces. In previous works [1, 2], we investigated invariance requirements to build some statistical tools on transformation groups and homogeneous manifolds that avoids paradoxes. In this paper, we consider finite dimensional manifolds with a Riemannian metric as the basic structure. Based on this metric, we develop the notions of mean value and covariance matrix of a random element, normal law, Mahalanobis distance and ?2 law. We provide a new proof of the characterization of Riemannian centers of mass and an original gradient descent algorithm to efficiently compute them. The notion of Normal law we propose is based on the maximization of the entropy knowing the mean and covariance of the distribution. The resulting family of pdfs spans the whole range from uniform (on compact manifolds) to the point mass distribution. Moreover, we were able to provide tractable approximations (with their limits) for small variances which show that we can effectively implement and work with these definitions.
804 citations
01 Jul 2006
TL;DR: An image deformation method based on Moving Least Squares using various classes of linear functions including affine, similarity and rigid transformations that yield fast deformations, which can be performed in real-time.
Abstract: We provide an image deformation method based on Moving Least Squares using various classes of linear functions including affine, similarity and rigid transformations. These deformations are realistic and give the user the impression of manipulating real-world objects. We also allow the user to specify the deformations using either sets of points or line segments, the later useful for controlling curves and profiles present in the image. For each of these techniques, we provide simple closed-form solutions that yield fast deformations, which can be performed in real-time.
684 citations
TL;DR: It is shown that the class of admissible affine state feedback control policies with knowledge of prior states is equivalent to the classOf admissible feedback policies that are affine functions of the past disturbance sequence, which implies that a broad class of constrained finite horizon robust and optimal control problems can be solved in a computationally efficient fashion using convex optimization methods.
617 citations
07 May 2006
TL;DR: In this paper, the authors cast the problem of motion segmentation of feature trajectories as linear manifold finding problems, and propose a general framework to segment a wide range of motions including independent, articulated, rigid, nonrigid, degenerate, non-degenerate or any combination of them.
Abstract: We cast the problem of motion segmentation of feature trajectories as linear manifold finding problems and propose a general framework for motion segmentation under affine projections which utilizes two properties of trajectory data: geometric constraint and locality. The geometric constraint states that the trajectories of the same motion lie in a low dimensional linear manifold and different motions result in different linear manifolds; locality, by which we mean in a transformed space a data and its neighbors tend to lie in the same linear manifold, provides a cue for efficient estimation of these manifolds. Our algorithm estimates a number of linear manifolds, whose dimensions are unknown beforehand, and segment the trajectories accordingly. It first transforms and normalizes the trajectories; secondly, for each trajectory it estimates a local linear manifold through local sampling; then it derives the affinity matrix based on principal subspace angles between these estimated linear manifolds; at last, spectral clustering is applied to the matrix and gives the segmentation result. Our algorithm is general without restriction on the number of linear manifolds and without prior knowledge of the dimensions of the linear manifolds. We demonstrate in our experiments that it can segment a wide range of motions including independent, articulated, rigid, non-rigid, degenerate, non-degenerate or any combination of them. In some highly challenging cases where other state-of-the-art motion segmentation algorithms may fail, our algorithm gives expected results.
579 citations
TL;DR: A novel representation for three-dimensional objects in terms of local affine-invariant descriptors of their images and the spatial relationships between the corresponding surface patches is introduced, allowing the acquisition of true 3D affine and Euclidean models from multiple unregistered images, as well as their recognition in photographs taken from arbitrary viewpoints.
Abstract: This article introduces a novel representation for three-dimensional (3D) objects in terms of local affine-invariant descriptors of their images and the spatial relationships between the corresponding surface patches. Geometric constraints associated with different views of the same patches under affine projection are combined with a normalized representation of their appearance to guide matching and reconstruction, allowing the acquisition of true 3D affine and Euclidean models from multiple unregistered images, as well as their recognition in photographs taken from arbitrary viewpoints. The proposed approach does not require a separate segmentation stage, and it is applicable to highly cluttered scenes. Modeling and recognition results are presented.
458 citations
TL;DR: In this article, a deformable registration algorithm for diffusion tensor MR images is presented that enables explicit optimization of tensor reorientation. But the objective function captures both the image similarity and the smoothness of the transformation across region boundaries.
393 citations
TL;DR: A family of techniques that are called congealing for modeling image classes from data to eliminate "nuisance" variables such as affine deformations from handwritten digits or unwanted bias fields from magnetic resonance images is presented.
Abstract: This paper presents a family of techniques that we call congealing for modeling image classes from data. The idea is to start with a set of images and make them appear as similar as possible by removing variability along the known axes of variation. This technique can be used to eliminate "nuisance" variables such as affine deformations from handwritten digits or unwanted bias fields from magnetic resonance images. In addition to separating and modeling the latent images - i.e., the images without the nuisance variables - we can model the nuisance variables themselves, leading to factorized generative image models. When nuisance variable distributions are shared between classes, one can share the knowledge learned in one task with another task, leading to efficient learning. We demonstrate this process by building a handwritten digit classifier from just a single example of each class. In addition to applications in handwritten character recognition, we describe in detail the application of bias removal from magnetic resonance images. Unlike previous methods, we use a separate, nonparametric model for the intensity values at each pixel. This allows us to leverage the data from the MR images of different patients to remove bias from each other. Only very weak assumptions are made about the distributions of intensity values in the images. In addition to the digit and MR applications, we discuss a number of other uses of congealing and describe experiments about the robustness and consistency of the method.
328 citations
Journal Article•
TL;DR: In this article, a generalized equation is proposed to represent a continuum of surface reconstruction solutions of a given non-integrable gradient field, where the range of solutions is related to the degree of anisotropy in applying weights to the gradient in the integration process.
Abstract: We propose a generalized equation to represent a continuum of surface reconstruction solutions of a given non-integrable gradient field. We show that common approaches such as Poisson solver and Frankot-Chellappa algorithm are special cases of this generalized equation. For a N x N pixel grid, the subspace of all integrable gradient fields is of dimension N 2 - 1. Our framework can be applied to derive a range of meaningful surface reconstructions from this high dimensional space. The key observation is that the range of solutions is related to the degree of anisotropy in applying weights to the gradients in the integration process. While common approaches use isotropic weights, we show that by using a progression of spatially varying anisotropic weights, we can achieve significant improvement in reconstructions. We propose (a) α-surfaces using binary weights, where the parameter a allows trade off between smoothness and robustness, (b) M-estimators and edge preserving regularization using continuous weights and (c) Diffusion using affine transformation of gradients. We provide results on photometric stereo, compare with previous approaches and show that anisotropic treatment discounts noise while recovering salient features in reconstructions.
313 citations
07 May 2006
TL;DR: A generalized equation to represent a continuum of surface reconstruction solutions of a given non-integrable gradient field is proposed and it is shown that common approaches such as Poisson solver and Frankot-Chellappa algorithm are special cases of this generalized equation.
Abstract: We propose a generalized equation to represent a continuum of surface reconstruction solutions of a given non-integrable gradient field. We show that common approaches such as Poisson solver and Frankot-Chellappa algorithm are special cases of this generalized equation. For a N × N pixel grid, the subspace of all integrable gradient fields is of dimension N2 – 1. Our framework can be applied to derive a range of meaningful surface reconstructions from this high dimensional space. The key observation is that the range of solutions is related to the degree of anisotropy in applying weights to the gradients in the integration process. While common approaches use isotropic weights, we show that by using a progression of spatially varying anisotropic weights, we can achieve significant improvement in reconstructions. We propose (a) α-surfaces using binary weights, where the parameter α allows trade off between smoothness and robustness, (b) M-estimators and edge preserving regularization using continuous weights and (c) Diffusion using affine transformation of gradients. We provide results on photometric stereo, compare with previous approaches and show that anisotropic treatment discounts noise while recovering salient features in reconstructions.
309 citations
TL;DR: In this paper, the authors studied the mirror symmetry of Calabi-Yau manifolds with singularities and showed an isomorphism between log complex moduli of a log CY space and the mirror of its mirror.
Abstract: This paper lays the foundations of a program to study mirror symmetry by studying the log structures of Illusie-Fontaine and Kato on degenerations of Calabi-Yau manifolds. The basic idea is that one can associate to certain sorts of degenerations of Calabi-Yau manifolds a log Calabi-Yau space, which is a log structure on the degenerate fibre. The log CY space captures essentially all the information of the degeneration, and hence all mirror statements for the "large complex structure limit" given by the degeneration can already be derived from the log CY space. In this paper we begin by discussing affine manifolds with singularities. Given such an affine manifold along with a polyhedral decomposition, we show how to construct a scheme consisting of a union of toric varieties. In certain non-degenerate cases, we can also construct log structures on these schemes. Conversely, given certain sorts of degenerations, one can build an affine manifold with singularities structure on the dual intersection complex of the degeneration. Mirror symmetry is then obtained as a discrete Legendre transform on these affine manifolds, thus providing an algebro-geometrization of the Strominger-Yau-Zaslow conjecture. The deepest result of this paper shows an isomorphism between log complex moduli of a log CY space and log Kahler moduli of its mirror.
245 citations
TL;DR: This work derives necessary and sufficient conditions for the existence of a multiaffine feedback control law keeping the system in a rectangular invariant and shows the application of its results to the problem of controlling the angular velocity of an aircraft with gas jet actuators.
Abstract: In this paper, we focus on a particular class of nonlinear affine control systems of the form xdot=f(x)+Bu, where the drift f is a multi-affine vector field (i.e., affine in each state component), the control distribution B is constant, and the control u is constrained to a convex set. For such a system, we first derive necessary and sufficient conditions for the existence of a multiaffine feedback control law keeping the system in a rectangular invariant. We then derive sufficient conditions for driving all initial states in a rectangle through a desired facet in finite time. If the control constraints are polyhedral, we show that all these conditions translate to checking the feasibility of systems of linear inequalities to be satisfied by the control at the vertices of the state rectangle. This work is motivated by the need to construct discrete abstractions for continuous and hybrid systems, in which analysis and control tasks specified in terms of reachability of sets of states can be reduced to searches on finite graphs. We show the application of our results to the problem of controlling the angular velocity of an aircraft with gas jet actuators
TL;DR: In this article, it was shown that almost bent and almost perfect polynomials are affine inequivalent to any sum of a power function and an affine function, and that they are almost perfect.
Abstract: New infinite classes of almost bent and almost perfect nonlinear polynomials are constructed. It is shown that they are affine inequivalent to any sum of a power function and an affine function
TL;DR: The careful and extensive experimental results show that this new model gives more compact representations for a wide variety of natural images under a wide range of signal-to-noise ratios than many existing methods, including wavelets.
Abstract: In this paper, we introduce a simple and efficient representation for natural images. We view an image (in either the spatial domain or the wavelet domain) as a collection of vectors in a high-dimensional space. We then fit a piece-wise linear model (i.e., a union of affine subspaces) to the vectors at each downsampling scale. We call this a multiscale hybrid linear model for the image. The model can be effectively estimated via a new algebraic method known as generalized principal component analysis (GPCA). The hybrid and hierarchical structure of this model allows us to effectively extract and exploit multimodal correlations among the imagery data at different scales. It conceptually and computationally remedies limitations of many existing image representation methods that are based on either a fixed linear transformation (e.g., DCT, wavelets), or an adaptive uni-modal linear transformation (e.g., PCA), or a multimodal model that uses only cluster means (e.g., VQ). We will justify both quantitatively and experimentally why and how such a simple multiscale hybrid model is able to reduce simultaneously the model complexity and computational cost. Despite a small overhead of the model, our careful and extensive experimental results show that this new model gives more compact representations for a wide variety of natural images under a wide range of signal-to-noise ratios than many existing methods, including wavelets. We also briefly address how the same (hybrid linear) modeling paradigm can be extended to be potentially useful for other applications, such as image segmentation
TL;DR: It is concluded that network fibril kinematics are not governed by affine principles, an important consideration in the understanding of tissue and TE mechanics, especially when load bearing is primarily by an interconnected fibrils network.
Abstract: The microstructure of tissues and tissue equivalents (TEs) plays a critical role in determining the mechanical properties thereof. One of the key challenges in constitutive modeling of TEs is incorporating the kinematics at both the macroscopic and the microscopic scale. Models of fibrous microstructure commonly assume fibrils to move homogeneously, that is affine with the macroscopic deformation. While intuitive for situations of fibril-matrix load transfer, the relevance of the affine assumption is less clear when primary load transfer is from fibril to fibril. The microstructure of TEs is a hydrated network of collagen fibrils, making its microstructural kinematics an open question. Numerical simulation of uniaxial extensile behavior in planar TE networks was performed with fibril kinematics dictated by the network model and by the affine model. The average fibril orientation evolved similarly with strain for both models. The individual fibril kinematics, however, were markedly different. There was no correlation between fibril strain and orientation in the network model, and fibril strains were contained by extensive reorientation. As a result, the macroscopic stress given by the network model was roughly threefold lower than the affine model. Also, the network model showed a toe region, where fibril reorientation precluded the development of significant fibril strain. We conclude that network fibril kinematics are not governed by affine principles, an important consideration in the understanding of tissue and TE mechanics, especially when load bearing is primarily by an interconnected fibril network.
TL;DR: In this article, a direct filtration-based maximum likelihood methodology for estimating the parameters and realizations of latent affine processes was developed, with a version of Bayes' rule used for recursively updating the joint characteristic function of latent variables and the data conditional upon past data.
Abstract: This article develops a direct filtration-based maximum likelihood methodology for estimating the parameters and realizations of latent affine processes. Filtration is conducted in the transform space of characteristic functions, with a version of Bayes’ rule used for recursively updating the joint characteristic function of latent variables and the data conditional upon past data. An application to daily stock returns over 1953-96 reveals substantial divergences from EMM-based estimates; in particular, more substantial and time-varying jump risk. The implications for stock index options’ prices are discussed.
TL;DR: In this article, a variational principle is used to minimize deviations in the magnitude of the magnetic induction equation constrained by an affine velocity profile, which depends linearly on coordinates, within a windowed subregion of the magnetogram sequence.
Abstract: The accurate estimation of magnetic footpoint velocities from a temporal sequence of photospheric magnetograms is critical for estimating the magnetic energy and helicity fluxes through the photosphere. A new technique for determining the magnetic footpoint velocities from a sequence of magnetograms is presented. This technique implements a variational principle to minimize deviations in the magnitude of the magnetic induction equation constrained by an affine velocity profile, which depends linearly on coordinates, within a windowed subregion of the magnetogram sequence. The variational principle produces an overdetermined system that is solved directly by linear least-squares or total least-squares methods. The resulting optical flow field and associated uncertainties are statistically consistent with the magnetic induction equation and the affine velocity profile within this aperture. The general technique has potential for application to other solar data sets where a physical model for the underlying image dynamics can be applied.
TL;DR: One of the key aims of this paper is to present results such that one can perform the relevant set computations using polyhedral algebra and computational geometry software, provided the system is piecewise affine and the constraints are polygonal.
Abstract: This paper presents new results that allow one to compute the set of states that can be robustly steered in a finite number of steps, via state feedback control, to a given target set. The assumptions that are made in this paper are that the system is discrete-time, nonlinear and time-invariant and subject to mixed constraints on the state and input. A persistent disturbance, dependent on the current state and input, acts on the system. Existing results are not able to address state- and input-dependent disturbances and the results in this paper are, therefore, a generalization of previously published results. One of the key aims of this paper is to present results such that one can perform the relevant set computations using polyhedral algebra and computational geometry software, provided the system is piecewise affine and the constraints are polygonal. Existing methods are only applicable to piecewise affine systems that either have no control inputs or no disturbances, whereas the results in this paper remove this limitation. Some simple examples are also given that show that, even if all the relevant sets are convex and the system is linear, convexity of the set of controllable states cannot be guaranteed.
01 Jan 2006
TL;DR: This work proposes a hybrid retinal image registration approach for ETDRS images that effectively combines both area-based and feature-based methods and uses two types of features, landmark points and sampling points, for affine/quadratic model estimation.
Abstract: This work studies retinal image registration in the context of the National Institutes of Health (NIH) Early Treatment Diabetic Retinopathy Study (ETDRS) standard. The ETDRS imaging protocol specifies seven fields of each retina and presents three major challenges for the image registration task. First, small overlaps between adjacent fields lead to inadequate landmark points for feature-based methods. Second, the non-uniform contrast/intensity distributions due to imperfect data acquisition will deteriorate the performance of area-based techniques. Third, high-resolution images contain large homogeneous nonvascular/texureless regions that weaken the capabilities of both feature-based and area-based techniques. In this work, we propose a hybrid retinal image registration approach for ETDRS images that effectively combines both area-based and feature-based methods. Four major steps are involved. First, the vascular tree is extracted by using an efficient local entropy-based thresholding technique. Next, zeroth-order translation is estimated by maximizing mutual information based on the binary image pair (area-based). Then image quality assessment regarding the ETDRS field definition is performed based on the translation model. If the image pair is accepted, higher-order transformations will be involved. Specifically, we use two types of features, landmark points and sampling points, for affine/quadratic model estimation. Three empirical conditions are derived experimentally to control the algorithm progress, so that we can achieve the lowest registration error and the highest success rate. Simulation results on 504 pairs of ETDRS images show the effectiveness and robustness of the proposed algorithm
TL;DR: In this article, the authors considered the problem of optimal control of switched piecewise affine autonomous systems, where the objective is to minimize a performance index over an infinite time horizon.
Abstract: This paper deals with optimal control of switched piecewise affine autonomous systems, where the objective is to minimize a performance index over an infinite time horizon. We assume that the switching sequence has a finite length, and that the decision variables are the switching instants and the sequence of operating modes. We present two different approaches for solving such an optimal control problem. The first approach iterates between a procedure that finds an optimal switching sequence of modes, and a procedure that finds the optimal switching instants. The second approach is inspired by dynamic programming and identifies the regions of the state space where an optimal mode switch should occur, therefore providing a state feedback control law.
TL;DR: In this article, a complete description of normal affine varieties with effective algebraic torus action in terms of what we call proper polyhedral divisors on semiprojective varieties is provided.
Abstract: We provide a complete description of normal affine varieties with effective algebraic torus action in terms of what we call proper polyhedral divisors on semiprojective varieties. Our approach extends classical cone constructions of Dolgachev, Demazure and Pinkham to the multigraded case, and it comprises the theory of affine toric varieties.
TL;DR: A general-purpose registration algorithm for medical images and volumes built upon a differential multiscale framework and incorporates the expectation maximization algorithm, showing that this approach is highly effective in registering a range of synthetic and clinical medical images.
TL;DR: In this paper, the problem of adaptive observer design for the class of state affine systems is discussed, based on recent results on adaptive observer with exponential rate of convergence obtained for multi-input-multi-output linear time varying systems on the one hand, and the well-known Kalman-like design for state affines on the other.
Abstract: In this paper, the problem of adaptive observer design for the class of state affine systems is discussed. The discussion is based on recent results on adaptive observer with exponential rate of convergence obtained for multi-input–multi-output linear time varying systems on the one hand, and the well-known Kalman-like design for state affine systems on the other. In particular the relationship between both designs is emphasized, showing how they can even be equivalent. The interest of such an adaptive observer for state affine systems is illustrated by the example of state and parameter estimation for the Lorenz chaotic system. The observer performances are illustrated via simulation.
TL;DR: A method for automatically obtaining object representations suitable for retrieval from generic video shots that includes associating regions within a single shot to represent a deforming object and an affine factorization method that copes with motion degeneracy.
Abstract: We describe a method for automatically obtaining object representations suitable for retrieval from generic video shots. The object representation consists of an association of frame regions. These regions provide exemplars of the object's possible visual appearances.
Two ideas are developed: (i) associating regions within a single shot to represent a deforming object; (ii) associating regions from the multiple visual aspects of a 3D object, thereby implicitly representing 3D structure. For the association we exploit temporal continuity (tracking) and wide baseline matching of affine covariant regions.
In the implementation there are three areas of novelty: First, we describe a method to repair short gaps in tracks. Second, we show how to join tracks across occlusions (where many tracks terminate simultaneously). Third, we develop an affine factorization method that copes with motion degeneracy.
We obtain tracks that last throughout the shot, without requiring a 3D reconstruction. The factorization method is used to associate tracks into object-level groups, with common motion. The outcome is that separate parts of an object that are not simultaneously visible (such as the front and back of a car, or the front and side of a face) are associated together. In turn this enables object-level matching and recognition throughout a video.
We illustrate the method on the feature film "Groundhog Day." Examples are given for the retrieval of deforming objects (heads, walking people) and rigid objects (vehicles, locations).
17 Jun 2006
TL;DR: A Riemannian geometric framework to compute averages and distributions of point configurations so that different configurations up to affine transformations are considered to be the same.
Abstract: This paper proposes a Riemannian geometric framework to compute averages and distributions of point configurations so that different configurations up to affine transformations are considered to be the same. The algorithms are fast and proven to be robust both theoretically and empirically. The utility of this framework is shown in a number of affine invariant clustering algorithms on image point data.
TL;DR: In this paper, a general affine Markov semigroup is formulated as the convolution of a homogeneous one with a skew convolution semigroup, and sufficient conditions for the regularities of the homogeneous affine semigroup and the skew semigroup are provided.
Abstract: A general affine Markov semigroup is formulated as the convolution of a homogeneous one with a skew convolution semigroup. We provide some sufficient conditions for the regularities of the homogeneous affine semigroup and the skew convolution semigroup. The corresponding affine Markov process is constructed as the strong solution of a system of stochastic equations with non-Lipschitz coefficients and Poisson-type integrals over some random sets. Based on this characterization, it is proved that the affine process arises naturally in a limit theorem for the difference of a pair of reactant processes in a catalytic branching system with immigration.
TL;DR: A new and conceptually simple semidefinite relaxation approach is proposed for MIMO detection in communication systems employing high-order QAM constellations that affords improved detection performance compared to existing solutions of comparable worst-case complexity order.
Abstract: A new and conceptually simple semidefinite relaxation approach is proposed for MIMO detection in communication systems employing high-order QAM constellations. The new approach affords improved detection performance compared to existing solutions of comparable worst-case complexity order, which is nearly cubic in the dimension of the transmitted symbol vector and independent of the constellation order for uniform QAM, or affine in the constellation order for nonuniform QAM
TL;DR: The affine Schur functions as discussed by the authors generalize the k-Schur functions of Lapointe, Lascoux and Morse as well as the cylindric Schur function of Postnikov.
Abstract: We define a new family [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="01i"/] of generating functions for w ∈ [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="02i"/] which are affine analogues of Stanley symmetric functions. We establish basic properties of these functions including symmetry, dominance and conjugation. We conjecture certain positivity properties in terms of a subfamily of symmetric functions called affine Schur functions. As applications, we show how affine Stanley symmetric functions generalize the (dual of the) k -Schur functions of Lapointe, Lascoux and Morse as well as the cylindric Schur functions of Postnikov. Conjecturally, affine Stanley symmetric functions should be related to the cohomology of the affine flag variety.
TL;DR: In this paper, the authors presented an example of quantum process tomography (QPT) performed on a single solid-state qubit using two energy levels of the triplet state in the nitrogen vacancy defect in diamond.
Abstract: We present an example of quantum process tomography (QPT) performed on a single solid-state qubit. The qubit used is two energy levels of the triplet state in the nitrogen vacancy defect in diamond. QPT is applied to a qubit which has been allowed to decohere for three different time periods. In each case, the process is found in terms of the χ matrix representation and the affine map representation. The discrepancy between experimentally estimated process and the closest physically valid process is noted. The results of QPT performed after three different decoherence times are used to find the error generators, or Lindblad operators, for the system, using the technique introduced by Boulant et al (2003 Phys. Rev. A 67 042322).
13 Feb 2006
TL;DR: This paper introduces into LLAH an affine invariant instead of the perspective invariant so as to improve its adjustability and experimental results show that the use of the affines enables us to improve either the accuracy from 96.2% to 97.8%, or the retrieval time from 112 msec./query to 75 msec./ query by selecting parameters of processing.
Abstract: Camera-based document image retrieval is a task of searching document images from the database based on query images captured using digital cameras. For this task, it is required to solve the problem of “perspective distortion” of images,as well as to establish a way of matching document images efficiently. To solve these problems we have proposed a method called Locally Likely Arrangement Hashing (LLAH) which is characterized by both the use of a perspective invariant to cope with the distortion and the efficiency: LLAH only requires O(N) time where N is the number of feature points that describe the query image. In this paper, we introduce into LLAH an affine invariant instead of the perspective invariant so as to improve its adjustability. Experimental results show that the use of the affine invariant enables us to improve either the accuracy from 96.2% to 97.8%, or the retrieval time from 112 msec./query to 75 msec./query by selecting parameters of processing.
TL;DR: In this paper, a coarse-fine search method based on an affine transform and a new technique of fine searching called "nested fine search method" is proposed for image correlation analysis.