Weak Perspective Research Articles

Detecting people in dense crowds

We propose a scheme to detect individuals in any image frame of a video sequence showing densely crowded scenes against cluttered backgrounds. The method uses only spatial information, and in an initial pass through the image a trained Viola–Jones-type local detector is used to locate individuals in the densely crowded scene. This yields a large number of false alarms. Hence, in a second step, we seek to reduce the false alarms, and propose two methods for this. In the first, color information from the initially detected windows is passed to a classifier to reduce the false alarms. This classifier consists of a cascade of boosted classifiers with Haar-like features as input and is trained with color information from local windows. In the second method, a weak perspective model of an uncalibrated camera is used to further reduce the false alarm rate while maintaining the detection rate. This is based on the size and locations of the detections in the image frame, without the use of any 3D world information. Results are presented in the form of receiver operating characteristic curves. For instance, at a 79.0% detection accuracy, the false alarm rate is 20.3%.

Governance Reforms and Rural Women in India: What Types of Women Citizens are Produced by the Will to Empower?

In 1993, the Government of India reserved one-third of the seats in rural councils (panchayats) for women, and along with NGOs, set up programs to empower rural women. We examine the usefulness of a Foucauldian governmentality framework in analyzing how women participants in panchayati raj institutions in Pune District, India, have been produced and the ways in which they respond. We conclude that the emphasis of a strong Foucauldian perspective on structure at the expense of agency obscures the complexity of women's responses. In contrast, a weak Foucauldian perspective is able to recognize that in some cases these incorporation processes create assertive, reformist, and resourceful citizens.

Iterative algorithm for optimal fiducials under weak perspective projection

AbstractIn previous work, we designed space fiducials with the aim of making camera pose determination as noise‐insensitive as possible. These fiducials turned out to be sets of points that formed concentric regular polyhedra. Here, we apply an idea of Dementhon and Davis and test and analyze an iterative linear algorithm in conjunction with our optimal fiducials to increase the accuracy of the computed camera pose. We also analyze under what circumstances this iterative algorithm is guaranteed to converge to the correct solution. Comprehensive computer simulations illustrate the behavior of the algorithm and the degree of improvement in pose determination in case of convergence. © 2009 Wiley Periodicals, Inc. Int J Imaging Syst Technol, 19, 27–36, 2009

3D Target Scale Estimation and Target Feature Separation for Size Preserving Tracking in PTZ Video

To achieve size preserving tracking, in addition to controlling the camera's pan and tilt motions to keep the object of interest in the camera's field of view (FOV), the camera's focal length is adjusted automatically to compensate for the changes in the target's image size caused by the relative motion between the camera and the target. The estimation accuracy of these changes determines the effectiveness of the resulting zoom control. The existing method of choice for real-time target scale estimation applies structure from motion (SFM) based on the weak perspective projection model. In this paper we propose a target scale estimation algorithm with a linear solution based on the more advanced paraperspective projection model, which improves the accuracy of scale estimation by considering center offset. Another key issue in SFM based algorithms is the separation of target and background features, especially when composite camera (pan/tilt/zoom) and target motions are involved. This paper designs a fast target feature separation/grouping algorithm, the 3D affine shape method. The resulting separation automatically adapts to the target's 3D geometry and motion and is able to accommodate a large amount of off-plane rotation, which most existing separation/grouping algorithms find difficult to achieve. Experimental results illustrate the effectiveness of the proposed scale estimation and feature separation algorithms in tracking translating and rotating objects with a PTZ camera while preserving their sizes. In comparison with the leading size preserving tracking algorithm described by Tordoff and Murray, our algorithm is able to reduce the cumulative tracking error significantly from 17.4% to 3.3%.

Robust Factorization Methods Using a Gaussian/Uniform Mixture Model

In this paper we address the problem of building a class of robust factorization algorithms that solve for the shape and motion parameters with both affine (weak perspective) and perspective camera models. We introduce a Gaussian/uniform mixture model and its associated EM algorithm. This allows us to address robust parameter estimation within a data clustering approach. We propose a robust technique that works with any affine factorization method and makes it robust to outliers. In addition, we show how such a framework can be further embedded into an iterative perspective factorization scheme. We carry out a large number of experiments to validate our algorithms and to compare them with existing ones. We also compare our approach with factorization methods that use M-estimators.

Incremental approach to shape recovery and registration from a sequence of images

This paper proposes an incremental shape recovery and registration method based on weak perspective factorization and pairwise point cloud registration. While a camera is moving freely in unknown environments, point features are automatically extracted and tracked. The 3-D position of scene points is then estimated using the tracked features from four consecutive frames and the point set is immediately registered to the global point cloud. The advantage of the proposed incremental method is that the recovery and registration process relies only on past frames for estimating a global shape. Shape recovery and registration are unified into a single framework where all the internal steps are linear and non-iterative. An application can utilize intermediate results that are incrementally computed from past frames and thus the procedure is applicable to on-line interactive vision systems such as augmented reality applications. Experimental results on several real image sequences showing the feasibility of the proposed approach are also provided.

Recovery of a linear model parameter using three vanishing points from a single image of weak perspective projection

An essential role of model-based vision deals with the problem of solving for the values of all viewpoint and model parameters to be computed for the dimensions of an object for a three-dimensional (3-D) model. We propose a new method using only three vanishing points for recovering the dimensions of an object, its position, and the focal length of the camera from a single image of weak perspective projection. Our aim is to compute the dimension vector v of a model represented by the unit vector of objects from the image. The optimization of the dimension vector v for the object can be thus solved by the standard nonlinear optimization techniques with a multistart method that generates multiple starting points for the optimizer by sampling the parameter space uniformly. Experimental results demonstrate the dimension vector v of the proposed method for the 3-D model and show that the performance of the proposed method is better than the conventional. We also address that the actual dimensions of object from the image agree well with the simulated results from the single image of weak perspective projection.

Multi-View AAM Fitting and Construction.

Active Appearance Models (AAMs) are generative, parametric models that have been successfully used in the past to model deformable objects such as human faces. The original AAMs formulation was 2D, but they have recently been extended to include a 3D shape model. A variety of single-view algorithms exist for fitting and constructing 3D AAMs but one area that has not been studied is multi-view algorithms. In this paper we present multi-view algorithms for both fitting and constructing 3D AAMs.Fitting an AAM to an image consists of minimizing the error between the input image and the closest model instance; i.e. solving a nonlinear optimization problem. In the first part of the paper we describe an algorithm for fitting a single AAM to multiple images, captured simultaneously by cameras with arbitrary locations, rotations, and response functions. This algorithm uses the scaled orthographic imaging model used by previous authors, and in the process of fitting computes, or calibrates, the scaled orthographic camera matrices. In the second part of the paper we describe an extension of this algorithm to calibrate weak perspective (or full perspective) camera models for each of the cameras. In essence, we use the human face as a (non-rigid) calibration grid. We demonstrate that the performance of this algorithm is roughly comparable to a standard algorithm using a calibration grid. In the third part of the paper, we show how camera calibration improves the performance of AAM fitting.A variety of non-rigid structure-from-motion algorithms, both single-view and multi-view, have been proposed that can be used to construct the corresponding 3D non-rigid shape models of a 2D AAM. In the final part of the paper, we show that constructing a 3D face model using non-rigid structure-from-motion suffers from the Bas-Relief ambiguity and may result in a "scaled" (stretched/compressed) model. We outline a robust non-rigid motion-stereo algorithm for calibrated multi-view 3D AAM construction and show how using calibrated multi-view motion-stereo can eliminate the Bas-Relief ambiguity and yield face models with higher 3D fidelity.

Uncalibrated Factorization Using a Variable Symmetric Affine Camera

In order to reconstruct 3-D Euclidean shape by the Tomasi-Kanade factorization, one needs to specify an affine camera model such as orthographic, weak perspective, and paraperspective. We present a new method that does not require any such specific models. We show that a minimal requirement for an affine camera to mimic perspective projection leads to a unique camera model, called symmetric affine camera, which has two free functions. We determine their values from input images by linear computation and demonstrate by experiments that an appropriate camera model is automatically selected.

Structure and motion of nonrigid object under perspective projection

The paper focuses on the problem of structure and motion of nonrigid object from image sequence under perspective projection. Many previous methods on this problem utilize the extension technique of SVD factorization based on rank constraint to the tracking matrix, where the 3D shape of nonrigid object is expressed as a weighted combination of a set of shape bases. All these solutions are based on the assumption of Affine camera model. This assumption will become invalid and cause large reconstruction errors when the object is close to the camera. In this paper, we propose two algorithms, namely the linear recursive estimation and the nonlinear optimization, to extend these methods to general perspective camera model. Both algorithms are based on the shape and motion of weak perspective projection. The former one updates the solutions from weak perspective to perspective projection by refining the scalars corresponding to the projective depths recursively. The latter one is based on nonlinear optimization by minimizing the perspective reprojection residuals. Extensive experiments on simulated data and real image sequences are performed to validate the effectiveness of our new algorithms and noticeable improvements over the previous solutions are observed.

3-D model-based vehicle tracking

This paper aims at tracking vehicles from monocular intensity image sequences and presents an efficient and robust approach to three-dimensional (3-D) model-based vehicle tracking. Under the weak perspective assumption and the ground-plane constraint, the movements of model projection in the two-dimensional image plane can be decomposed into two motions: translation and rotation. They are the results of the corresponding movements of 3-D translation on the ground plane (GP) and rotation around the normal of the GP, which can be determined separately. A new metric based on point-to-line segment distance is proposed to evaluate the similarity between an image region and an instantiation of a 3-D vehicle model under a given pose. Based on this, we provide an efficient pose refinement method to refine the vehicle's pose parameters. An improved EKF is also proposed to track and to predict vehicle motion with a precise kinematics model. Experimental results with both indoor and outdoor data show that the algorithm obtains desirable performance even under severe occlusion and clutter.

A 3-D Vision-Based Man–Machine Interface For Hand-Controlled Telerobot

This work presents a robust telerobotic system that consists of a real-time vision-based operator hand tracking system (client) and a slave robot (server) which are interconnected through a LAN. The tracking system: 1) monitors the operator hand motion and 2) determines its position and orientation which are used to control the slave robot. Two digital cameras are used to monitor a four-ball-based feature frame that is held by the operator hand. To determine the three-dimensional (3-D) position a tracking algorithm based on uncalibrated cameras with weak perspective projection model is used. This allows finding 3-D differential position and orientation of the operator hand. The features of the proposed system are: 1) a metric for color matching to discriminate the balls from their background; 2) a uniform and spiral search approach to speed up the detection; 3) tracking in the presence of partial occlusion; 4) consolidate detection by using shape and geometric matching; and 5) dynamic update of the reference colors. The operator can see the effects of the previous motion which enables making the necessary corrections through repetitive operator hand-eye interactions. Evaluation shows that the static and dynamic errors of the tracking algorithm are 0.1% and 0.6% for a centered workspace of 20/sup 3/ in/sup 3/ that is 40-60 in away from the cameras. Running the tracking algorithm on two PCs in parallel allowed: 1) a parallel image grabbing delay of 60 ms; 2) a stereo matching delay of 50 ms; and 3) a global refresh rate of 9 Hz.

Reconstruction of a Scene with Multiple Linearly Moving Objects

In this paper we describe an algorithm to recover the scene structure, the trajectories of the moving objects and the camera motion simultaneously given a monocular image sequence. The number of the moving objects is automatically detected without prior motion segmentation. Assuming that the objects are moving linearly with constant speeds, we propose a unified geometrical representation of the static scene and the moving objects. This representation enables the embedding of the motion constraints into the scene structure, which leads to a factorization-based algorithm. We also discuss solutions to the degenerate cases which can be automatically detected by the algorithm. Extension of the algorithm to weak perspective projections is presented as well. Experimental results on synthetic and real images show that the algorithm is reliable under noise.

Viewpoint independent matching of planar curves in 3D space

We present a new approach to match planar curves using the weak perspective projection model. This is based on a set of shape parameters that can be extracted from a closed or open contour, derived from the original image as a θ( s) boundary code. In order to reduce the complexity and increase the robustness of the matching process, the original parameters are reduced to a set of three intermediate variables, each of which can be calculated independently. These variables are contained within a system of linear equations which define the angles and the ratio of the heights of corresponding point pairs on the two contours with respect to a floating coordinate system. The shape matching process is scale and orientation independent, and the original parameters that describe the relative pose of the two contours in 3D space can be recovered subsequently. The approach can be applied to “featured” and “featureless” contours, to whole and partial contours, and is demonstrated on images of contours and mechanical parts and tools to recover identity and pose.

Estimation of movement parameters of 3D textured surfaces using the autocorrelation function

We present a new method for computing the movement parameters of textured surfaces moving in a three dimensional environment. This method is based on the fact that the autocorrelation functions of an image and of its affine transformed version are linked by the same affine transformation applied to their axes. We use the Euler's angles and the weak perspective projection. We show how to compute directly the movement parameters by means of fourth-degree polynomials which model outlines extracted from the autocorrelation function. Experimental results are presented which support the effectiveness of the proposed approach.

Three-dimensional shape recovery across two views using approximate geometric constraints

We propose a new approach to object matching and shape reconstruction across two views. The approach relies on the topological relationship among the feature points and a planarity approximation for the object surfaces in carrying the object from the model view to the scene view. The correspondences are then refined by fitting an active contour model to the transferred feature points on the scene view, which automatically assumes the shape of the object on correct matching. For the purpose of 3-D reconstruction, it could be shown that while the establishment of such correct correspondences alone would result in ambiguities under the assumption of weak perspective projection, the adoption of a regularization criterion, in the form of a depth-continuity constraint, and a set of geometric constraints associated with selected subset of surfaces and contours of the object, would overcome this problem and lead to the recovery of the approximate 3-D structure of the object.

Trifocal tensors for weak perspective and paraperspective projections

Trilinear relationships among the image point coordinates obtained by perspective projection of several feature points over three views have been investigated, and it has been shown that seven point correspondences are sufficient to determine the coefficients involved. We show that analogous trilinear relationships exist for the weak perspective and paraperspective projections, and that only four point correspondences are necessary for the determination of the coefficients. When the trilinear relationships are known, the position of the image of a point in one camera system can be determined from its image in the two other camera systems through linear equations.

Image-Based Rendering Using Parameterized Image Varieties

This paper addresses the problem of characterizing the set of all images of a rigid set of m points and n lines observed by a weak perspective or paraperspective camera. By taking explicitly into a...

Robust stabilization of second-order image-based affine systems

In this paper, the problem of robust relative positioning between a 6-DOF robot camera and an object of interest is considered. Assuming weak perspective camera model and local linear approximation of visible object's surface, an image-based state space representation of robot camera–object interaction model is derived, based on the matrix of 2-D affine transformations. Dynamic extension of the visual model permits to estimate 3-D parameters directly as functions of state variables. The proposed nonlinear robust control law ensures asymptotic stability but at image singularities, assuming exact model and state measurements. In the presence of bounded uncertainties, under appropriate choice of control gains, ultimate boundedness of the state error is also formally proved. Simulation results validate the theoretical framework both in terms of system convergence and control robustness.

Digital X-ray stereophotogrammetry for cochlear implantation

Multielectrode, intracochlear implant systems are effective treatment for profound sensorineural hearing loss. In some cases, these systems do not perform well, which may be partially due to variations in implant location within the cochlea. Determination of each electrode's position in a patient's inner ear provides an in vivo basis for both the cochlear modeling of electrical fields and the future design of electrode arrays that deliver electrical stimulation to surviving auditory neurons, and may improve speech processor programming for better speech recognition. We developed an X-ray stereophotogrammetric approach to localize implanted electrodes in three dimensions. Stereophotogrammetry of implanted electrodes is formulated in weak perspective geometry, with knowledge of a three-dimensional (3-D) reference structure and electrode positions in each of two digital stereo-images. The localization error is theoretically, numerically, and experimentally quantified. Both numerical and experimental results demonstrate the feasibility of the technique.