Euclidean reconstruction from contour matches

Person re-identification is one of the most important and challenging problems in video analytics systems; it aims to match people across non-overlapping camera views. For person re-identification, metric learning is introduced to improve the performance by providing a metric adapted for cross-view matching. The essence of metric learning is to search for an optimal projection matrix to project the original features into a new feature space. However, most existing metric learning methods overlook the inconsistency of feature distributions in multiple cameras. In this paper, we propose a multi-projection metric learning (MPML) method to overcome the inconsistency among multiple cameras in person re-identification. Our solution is to jointly learn multiple projection matrices using paired samples from different cameras to project features from different cameras into a common feature space. To make our method adaptive to newly added cameras without affecting the learned projection matrices, we further propose an adaptive MPML method, which can learn new camera projection matrices without having to update any of the obtained projection matrices. The proposed methods are evaluated on four major person re-identification data sets, with comprehensive experiments showing the effectiveness of the proposed methods and notable improvements over the state-of-the–art approaches.

—By observing the descriptors of the contour points, correspondence based contour matching is widely used in pattern recognition. However, it is a pity that the correspondences established by descriptor matching are not reliably. In this paper, a matching approach, in which the inlier correspondences in matched configurations are used for voting, is proposed. Experimental results show that the proposed voting approach is well suited for contour point matching under affine transformation and noise. Keywords-affine, moment, point matching, voting I. I NTRODUCTION Contour matching is an important task in computer vision such as image analysis and pattern recognition. However, despite great effort, it is still a difficult problem especially when the contours are noise disturbed or distorted due to different viewpoint. It is well known that the deformations between shapes can be approximated by affine transformations if the viewpoints are far enough. Consequently, invariant to affine transformation is a desirable property for many contour matching problems. The contours, which are originally defined by x and y coordinates of points, contain considerable amount of information, and a number of contour matching methods have been suggested for contour recognition under affine transformation. Contour matching methods can be generally divided into two classes: feature-based methods [1-4] and correspondence-based methods. The classification is based on whether the correspondences between points are taken into account in contour matching. In the feature-based methods, such as shape signatures, curvature scale space, and R-histogram et al, the features are extracted as descriptors to measure the similarity between contours. In contrast to the feature-based methods, correspondence-based methods find the matched contours based on point-to-point matching. Hausdorff distance [5] is a classical correspondence-based method, in which Euclidean distance is used to locate contours. Belongie et al. recover the correspondences between two boundary point sets based on the shape context (SC) [6,7], which describes the distribution of the rest of the contour with respect to a given point on the contour. Moment, which can be treated as the description for the point, is one of the widely used technique works for point-to-point matching. One of the most widely used contour moment is FD [8], and has been extended to be affine invariant by Arbter et al. Yang and Cohen used a new set of cross-weighted moments to analytically solve for point matching. Liu et al proposed an generating function to derive various affine invariant moments. Wang et al [9] taken the diagonals of the orthogonal projection matrices are the contour moments. Once the cost of moment matching has been measured, the approach for point matching shall be followed. Generally, the matched points are considered to be the ones with the minimal matching cost. However, to subject to the constraint that the matching be one-to-one, dynamic programming (i.e. Hungarian) is always adopted. Though the ‘dummy’ nodes are added to point sets with a constant matching cost to have robust handling of outliers, there still exist outlier in the correspondences obtained by the Hungarian method. Therefore, to further improve the accuracy of point matching, a useful schema of outlier removal based on the monotonic property of contour correspondence has been proposed in [9]. The monotonic property implies that the ordering of points matching should be monotonic regardless of a specific indexing of the points. Motivated by [9], to remove the outliers in the correspondences, a novel point matching algorithm based on voting is suggested. As we known, since the moment is extracted from the configuration of the point, the matching of two point are actually the matching of two local configurations. Accordingly, the points in the configurations of two matched points are inlier correspondences. Then, the correspondences between configurations of two matched points can be used to validate the correspondence between the two points. The rest of the paper is organized as the follows. Section 2 describes a general system for point matching. The voting schema for outlier removal is suggested in Section 3. The experimental examples are given in Section 4, and Section 5 concluded the paper. II. C

In this paper, we present a new method for multi-view 3D reconstruction based on the use of a binocular stereo vision system constituted of two unattached cameras to initialize the reconstruction process. Afterwards , the second camera of stereo vision system (characterized by varying parameters) moves to capture more images at different times which are used to obtain an almost complete 3D reconstruction. The first two projection matrices are estimated by using a 3D pattern with known properties. After that, 3D scene points are recovered by triangulation of the matched interest points between these two images. The proposed approach is incremental. At each insertion of a new image, the camera projection matrix is estimated using the 3D information already calculated and new 3D points are recovered by triangulation from the result of the matching of interest points between the inserted image and the previous image. For the refinement of the new projection matrix and the new 3D points, a local bundle adjustment is performed. At first, all projection matrices are estimated, the matches between consecutive images are detected and Euclidean sparse 3D reconstruction is obtained. So, to increase the number of matches and have a more dense reconstruction, the Match propagation algorithm, more suitable for interesting movement of the camera, was applied on the pairs of consecutive images. The experimental results show the power and robustness of the proposed approach.

To present a generic geometric calibration method for tomographic imaging systems with flat-panel detectors in a very detailed manner, in the aim to provide a useful tool to the public domain. The method is based on a projection matrix which represents a mapping from 3D object coordinate system to 2D projection image plane. The projection matrix can be determined experimentally through the imaging of a phantom of known marker geometry. Accurate implementation was accomplished through direct computation algorithms, including a novel ellipse fitting using singular value decomposition and data normalization. Benefits of the method include: (1) It is capable of being applied to systems of different scan trajectories, source-detector alignments, and detector orientations; (2) projection matrices can be utilized in image reconstructions or in the extraction of explicit geometrical parameters; and (3) the method imposes minimal limits on the design of calibration phantom. C++ programs that calculate projection matrices and extract geometric parameters from them are also provided. For validation, the calibration method was applied to the computer simulation of a cone-beam CT system, as well as to three tomosynthesis prototypes of different source-detector movement patterns: Source and detector rotating synchronizedly; source rotating and detector wobbling; and source rotating and detector staying stationary. Projection matrices were computed on a view by view basis. Geometric parameters extracted from projection matrices were consistent with actual settings. Images were reconstructed by directly using projection matrices, and were compared to virtual Shepp-Logan image for CT simulation and to central projection images of CIRS breast phantoms for tomosynthesis prototypes. They showed no obvious distortion or blurring, indicating the high quality of geometric calibration results. When the computed central ray offsets were perturbed with Gaussian noises of 1 pixel standard deviation, the reconstructed image showed apparent distortion, which further demonstrated the accuracy of the geometric calibration method. The method is suitable for tomographic imaging systems with flat-panel detectors.

Purpose: To develop a high precision geometry calibration method and an efficient image reconstruction algorithm for digital tomosynthesis system. Method and Materials: A geometry calibration phantom was constructed with 40 markers arranged in two planes parallel to the breast holder. A 3×4 projection matrix which maps the coordinates (x,y,z) of a point in the object to the coordinates (u,v) of the correspondent projection point on the detector was constructed for each projection angle based on the projection images of the calibration phantom. All information for the system geometry, such as source-to-detector distance, source to ISO distance, central ray offset on the detector (u0, v0), and detector angle offsets, can be extracted from the projection matrices. The projection matrices, not explicit geometry parameters, were used in a modified Feldkamp algorithm to reconstruct the imaged object. A prototype tomosynthesis system and a CIRS anthropomorphic breast phantom with multiple embedded structures were used to test the geometry calibration accuracy and the reconstruction algorithm. Results: 3-D image of the breast phantom was reconstructed using the projection matrices. 4 fibers, 6 masses, and all 12 speck groups were visible in the focal plane. Conclusion: Geometry calibration based on the projection matrices is accurate and reconstruction using the projection matrices is efficient.

We present a technique for camera calibration and Euclidean reconstruction from multiple images of the same scene. Unlike standard Tsai's camera calibration from a known scene, we exploited controlled known motions of the camera to obtain its calibration and Euclidean reconstruction without any knowledge about the scene. We consider three linearly independent translations of an uncalibrated camera mounted on a robot arm that provides us with four views of the scene. The translations of the robot arm are measured in a robot coordinate system. This special, but still realistic, arrangement allowed us to find a linear algorithm for recovering all intrinsic camera calibration parameters, the rotation of the camera with respect to the robot coordinate system, and proper scaling factors for all points allowing their Euclidean reconstruction. The experiments showed that an efficient and robust algorithm was obtained by exploiting Total Least Squares in combination with careful normalization of image coordinates.

The central problem for most existing metric learning methods is to find a suitable projection matrix on the differences of all pairs of data points. However, a single unified projection matrix can hardly characterize all data similarities accurately as the practical data are usually very complicated, and simply adopting one global projection matrix might ignore important local patterns hidden in the dataset. To address this issue, this paper proposes a novel method dubbed “Data-Adaptive Metric Learning” (DAML), which constructs a data-adaptive projection matrix for each data pair by selectively combining a set of learned candidate matrices. As a result, every data pair can obtain a specific projection matrix, enabling the proposed DAML to flexibly fit the training data and produce discriminative projection results. The model of DAML is formulated as an optimization problem which jointly learns candidate projection matrices and their sparse combination for every data pair. Nevertheless, the over-fitting problem may occur due to the large amount of parameters to be learned. To tackle this issue, we adopt the Total Variation (TV) regularizer to align the scales of data embedding produced by all candidate projection matrices, and thus the generated metrics of these learned candidates are generally comparable. Furthermore, we extend the basic linear DAML model to the kernerlized version (denoted “KDAML”) to handle the non-linear cases, and the Iterative Shrinkage-Thresholding Algorithm (ISTA) is employed to solve the optimization model. Intensive experimental results on various applications including retrieval, classification, and verification clearly demonstrate the superiority of our algorithm to other state-of-the-art metric learning methodologies.

3D reconstruction of blood vessels is a powerful visualization tool for physicians, since it allows them to refer to qualitative representation of their subject of study. In this paper we propose a 3D reconstruction method of retinal vessels from fundus images. The reconstruction method propose herein uses images of the same retinal structure in epipolar geometry. Images are preprocessed by RISA system for segmenting blood vessels and obtaining feature points for correspondences. The correspondence points process is solved using correlation. The LMedS analysis and Graph Transformation Matching algorithm are used for outliers suppression. Camera projection matrices are computed with the normalized eight point algorithm. Finally, we retrieve 3D position of the retinal tree points by linear triangulation. In order to increase the power of visualization, 3D tree skeletons are represented by surfaces via generalized cylinders whose radius correspond to morphological measurements obtained by RISA. In this paper the complete calibration process including the fundus camera and the optical properties of the eye, the so called camera-eye system is proposed. On one hand, the internal parameters of the fundus camera are obtained by classical algorithms using a reference pattern. On the other hand, we minimize the undesirable efects of the aberrations induced by the eyeball optical system assuming that contact enlarging lens corrects astigmatism, spherical and coma aberrations are reduced changing the aperture size and eye refractive errors are suppressed adjusting camera focus during image acquisition. Evaluation of two self-calibration proposals and results of 3D blood vessel surface reconstruction are presented.

3D reconstruction of trees is an important task for tree analysis but the most affordable approach to capture real objects is with a camera. Although, there already exist methods for 3D reconstruction of trees from multiple photographs, they mostly handle only self-standing trees captured at narrow angles. In fact, dense feature detection and matching is in most cases only the first step of the reconstruction and requires a large set of features and high similarity between individual pictures. However, capturing trees in the orchard is in most cases possible only at wider angles between the individual pictures and with overlapping branches from other trees, which prevents reliable feature matching. We introduce a new approach for estimating projection matrices to produce 3D point clouds of trees from multiple photographs. By manually relating a smaller number of points on images to reference objects, we substitute the missing dense set of features. We assign to each image a projection matrix and minimize the projection error between the images and reference objects using simulated annealing. Thereby, we produce correct projection matrices for further steps in 3D reconstruction. Our approach is tested on a simple application for 3D reconstruction of trees to produce a 3D point cloud. We analyze convergence rates of the optimization and show that the proposed approach can produce feasible projection matrices from a sufficiently large set of feature points. In the future, this approach will be a part of a complete system for tree reconstruction and analysis.

In this paper, motor imagery electroencephalograph classification problem is investigated and a method which modifies the projection matrix is proposed based on common spatial pattern analysis. Exceptional samples are detected through examining the features generated by the projection matrix in the first place, which are special in terms that the projection matrix in common spatial pattern analysis fails to extract discriminant features from them. Projection matrices for exceptional trials are re-estimated and integrated together to form the final projection model. Based on this integrated model, feature extraction is carried out and classification follows by employing support vector machine. The validity of the proposed method is verified through experiment studies. Two data sets that consist of two classes are used, and results show that the proposed method generates more discriminant features.

In this paper we address the design of projection matrix for compressed sensing. In most compressed sensing applications, random projection matrices have been used but it has been shown that optimizing these projections can greatly improve the sparse signal reconstruction performance. An incoherent projection matrix can greatly reduce the recovery error for sparse signal reconstruction. With this motivation, we propose an algorithm for the construction of an incoherent projection matrix with respect to the designed equiangular tight frame (ETF) for reducing pairwise mutual coherence. The designed frame consists of a set of column vectors in a finite dimensional Hilbert space with the desired norm and reduced pairwise mutual coherence. The proposed method is based on updating ETF with inertial force and constructing incoherent frame and projection matrix using alternating minimization. We compare the performance of the proposed algorithm with state-of-the-art projection matrix design algorithms via numerical experiments and the results show that the proposed algorithm outperforms the other algorithms.

Reconciliation of process data using other projection matrices

Projection matrices in variable environments: λ1 in theory and practice

This paper presents a novel approach to both the calibration of the omnidirectional camera and the contour matching in architectural scenes. The proposed algorithm divides an entire image into several sub-regions, and then examines the number of the inliers in each sub-region and the area of each region. In our method, the standard deviations are used as quantitative measure to select a proper inlier set. Since the line segments of man-made objects are projected to contours in omnidirectional images, contour matching problem is important for more precise camera recovery. We propose a novel contour matching method using geometrical information of the omnidirectional camera.

A number of recent papers have demonstrated that camera “self-calibration” can be accomplished purely from image measurements, without requiring special calibration objects or known camera motion. We describe a method, based on self-calibration, for obtaining (scaled) Euclidean structure from multiple uncalibrated perspective images using only point matches between views. The method is in two stages. First, using an uncalibrated camera, structure is recovered up to an affine ambiguity from two views. Second, from one or more further views of this affine structure the camera intrinsic parameters are determined, and the structure ambiguity reduced to scaled Euclidean. The technique is independent of how the affine structure is obtained. We analyse its limitations and degeneracies. Results are given for images of real scenes. An application is described for active vision, where a Euclidean reconstruction is obtained during normal operation with an initially uncalibrated camera. Finally, it is demonstrated that Euclidean reconstruction can be obtained from a single perspective image of a repeated structure