Chains are vector-valued signals sampling a curve. They are important to motion signal processing and to many scientific applications including location sensors. We propose a novel measure of smoothness for chains curves by generalizing the scalar-valued concept of monotonicity. Monotonicity can be defined by the connectedness of the inverse image of balls. This definition is coordinate-invariant and can be computed efficiently over chains. Monotone curves can be discontinuous, but continuous monotone curves are differentiable a.e. Over chains, a simple sphere-preserving filter shown to never decrease the degree of monotonicity. It outperforms moving average filters over a synthetic data set. Applications include Time Series Segmentation, chain reconstruction from unordered data points, Optical Character Recognition, and Pattern Matching.
A motion signal is comprised of two components: orientation and translation. The orientation vector indicates where the object is facing, whereas the translation component determines the object's location. Recent work has focused on smoothing the orientation vectors @cite_2 @cite_16 , whereas the results of the present paper apply equally well to orientation vectors (points on the surface of a unit sphere) as to arbitrary translation signals.
@cite_16 @cite_2
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Smooth motion generation is an important issue in the computer animation and virtual reality areas. The motion of a rigid body consists of translation and orientation. The former is described by a space curve in 3-dimensional Euclidean space, while the latter is represented by a curve in the unit quaternion space. Although there exist well-known techniques for smoothing the translation data, smoothing the orientation data is yet to be explored due to the nonlinearity of the unit quaternion space. This paper presents a wavelet-based algorithm for smoothing noise-embedded motion data and the experiment shows the effectiveness of the proposed algorithm. The problem considered involves the use of a sequence of noisy monocular images of a three-dimensional moving object to estimate both its structure and kinematics. The object is assumed to be rigid, and its motion is assumed to be smooth. A set of object match points is assumed to be available, consisting of fixed features on the object, the image plane coordinates of which have been extracted from successive images in the sequence. Structure is defined as the 3-D positions of these object feature points, relative to each other. Rotational motion occurs about the origin of an object-centered coordinate system, while translational motion is that of the origin of this coordinate system. In this work, which is a continuation of the research done by the authors and reported previously (ibid., vol.PAMI-8, p.90-9, Jan. 1986), results of an experiment with real imagery are presented, involving estimation of 28 unknown translational, rotational, and structural parameters, based on 12 images with seven feature points. > The error sensitivity in the estimation of the 3-D motion and the normal of a planar surface from an instantaneous motion field is studied. The statistical theory or the Cramer-Rao lower bound is used for error covariance in the estimated motion and structure parameters. This enables the derivation of results valid for any unbiased estimator under the assumption of Gaussian noise in the motion field. The obtained lower-bound-matrix is studied analytically with respect to measurement noise, size of the field of view, and the motion-geometry configuration. The coupling between translation and rotation is exacerbated if the field of view and the slant of the plane become smaller, and the deviation of the translation from the viewing direction becomes larger. The relationships of the uncertainty bounds for every unknown motion parameter to the angle between translation and the plane-normal, the size of the field of view, and the distance from the perceived plane and the translation magnitude are discussed. > Inspired by Weber's Law, this paper proposes a simple, yet very powerful and robust local descriptor, called the Weber Local Descriptor (WLD). It is based on the fact that human perception of a pattern depends not only on the change of a stimulus (such as sound, lighting) but also on the original intensity of the stimulus. Specifically, WLD consists of two components: differential excitation and orientation. The differential excitation component is a function of the ratio between two terms: One is the relative intensity differences of a current pixel against its neighbors, the other is the intensity of the current pixel. The orientation component is the gradient orientation of the current pixel. For a given image, we use the two components to construct a concatenated WLD histogram. Experimental results on the Brodatz and KTH-TIPS2-a texture databases show that WLD impressively outperforms the other widely used descriptors (e.g., Gabor and SIFT). In addition, experimental results on human face detection also show a promising performance comparable to the best known results on the MIT+CMU frontal face test set, the AR face data set, and the CMU profile test set. The detection of moving objects is important in many tasks. This paper examines moving object detection based primarily on optical flow. We conclude that in realistic situations, detection using visual information alone is quite difficult, particularly when the camera may also be moving. The availability of additional information about camera motion and or scene structure greatly simplifies the problem. Two general classes of techniques are examined. The first is based upon the motion epipolar constraint—translational motion produces a flow field radially expanding from a “focus of expansion” (FOE). Epipolar methods depend on knowing at least partial information about camera translation and or rotation. The second class of methods is based on comparison of observed optical flow with other information about depth, for example from stereo vision. Examples of several of these techniques are presented. This paper deals with the determination of the position and orientation of a mobile robot from distance measurements provided by a belt of onboard ultrasonic sensors. The environment is assumed to be two-dimensional, and a map of its landmarks is available to the robot. In this context, classical localization methods have three main limitations. First, each data point provided by a sensor must be associated with a given landmark. This data-association step turns out to be extremely complex and time-consuming, and its results can usually not be guaranteed. The second limitation is that these methods are based on linearization, which makes them inherently local. The third limitation is their lack of robustness to outliers due, e.g., to sensor malfunctions or outdated maps. By contrast, the method proposed here, based on interval analysis, bypasses the data-association step, handles the problem as nonlinear and in a global way and is (extraordinarily) robust to outliers. A calibration algorithm of two cameras using observations of a moving person is presented. Similar methods have been proposed for self-calibration with a single camera, but internal parameter estimation is only limited to the focal length. Recently it has been demonstrated that principal point supposed in the center of the image causes inaccuracy of all estimated parameters. Our method exploits two cameras, using image points of head and foot locations of a moving person, to determine for both cameras the focal length and the principal point. Moreover with the increasing number of cameras there is a demand of procedures to determine their relative placements. In this paper we also describe a method to find the relative position and orientation of two cameras: the rotation matrix and the translation vector which describe the rigid motion between the coordinate frames fixed in two cameras. Results in synthetic and real scenes are presented to evaluate the performance of the proposed method. We present a task-parameterized probabilistic model encoding movements in the form of virtual spring-damper systems acting in multiple frames of reference. Each candidate coordinate system observes a set of demonstrations from its own perspective, by extracting an attractor path whose variations depend on the relevance of the frame at each step of the task. This information is exploited to generate new attractor paths in new situations (new position and orientation of the frames), with the predicted covariances used to estimate the varying stiffness and damping of the spring-damper systems, resulting in a minimal intervention control strategy. The approach is tested with a 7-DOFs Barrett WAM manipulator whose movement and impedance behavior need to be modulated in regard to the position and orientation of two external objects varying during demonstration and reproduction. Neuronal representation and extraction of spatial information are essential for behavioral control. For flying insects, a plausible way to gain spatial information is to exploit distancedependent optic flow that is generated during translational self-motion. Optic flow is computed by arrays of local motion detectors retinotopically arranged in the second neuropile layer of the insect visual system. These motion detectors have adaptive response characteristics, i.e. their responses to motion with a constant or only slowly changing velocity decrease, while their sensitivity to rapid velocity changes is maintained or even increases. We analyzed by a modeling approach how motion adaptation affects signal representation at the output of arrays of motion detectors during simulated flight in artificial and natural 3D environments. We focused on translational flight, because spatial information is only contained in the optic flow induced by translational locomotion. Indeed, flies, bees and other insects segregate their flight into relatively long intersaccadic translational flight sections interspersed with brief and rapid saccadic turns, presumably to maximize periods of translation (80 of the flight). With a novel adaptive model of the insect visual motion pathway we could show that the motion detector responses to background structures of cluttered environments are largely attenuated as a consequence of motion adaptation, while responses to foreground objects stay constant or even increase. This conclusion even holds under the dynamic flight conditions of insects. Abstract A procedure for processing real world image sequences produced by relative translational motion between a sensor and environmental objects is presented. In this procedure, the determination of the direction of sensor translation is effectively combined with the determination of the displacement of image features and environmental depth. It requires no restrictions on the direction of motion, nor the location and shape of environmental objects. It has been applied successfully to real-world image sequences from several different task domains. The processing consists of two basic steps: feature extraction and search. The feature extraction process picks out small image areas which may correspond to distinguishing parts of environmental objects. The direction of translational motion is then found by a search which determines the image displacement paths along which a measure of feature mismatch is minimized for a set of features. The correct direction of translation will minimize this error measure and also determine the corresponding image displacement paths for which the extracted features match well. Motion segmentation based on point trajectories can integrate information of a whole video shot to detect and separate moving objects. Commonly, similarities are defined between pairs of trajectories. However, pairwise similarities restrict the motion model to translations. Non-translational motion, such as rotation or scaling, is penalized in such an approach. We propose to define similarities on higher order tuples rather than pairs, which leads to hypergraphs. To apply spectral clustering, the hypergraph is transferred to an ordinary graph, an operation that can be interpreted as a projection. We propose a specific nonlinear projection via a regularized maximum operator, and show that it yields significant improvements both compared to pairwise similarities and alternative hypergraph projections. Motion is a strong cue for unsupervised object-level grouping. In this paper, we demonstrate that motion will be exploited most effectively, if it is regarded over larger time windows. Opposed to classical two-frame optical flow, point trajectories that span hundreds of frames are less susceptible to short-term variations that hinder separating different objects. As a positive side effect, the resulting groupings are temporally consistent over a whole video shot, a property that requires tedious post-processing in the vast majority of existing approaches. We suggest working with a paradigm that starts with semi-dense motion cues first and that fills up textureless areas afterwards based on color. This paper also contributes the Freiburg-Berkeley motion segmentation (FBMS) dataset, a large, heterogeneous benchmark with 59 sequences and pixel-accurate ground truth annotation of moving objects. A method for the determination of camera location from two-dimensional (2-D) to three-dimensional (3-D) straight line or point correspondences is presented. With this method, the computations of the rotation matrix and the translation vector of the camera are separable. First, the rotation matrix is found by a linear algorithm using eight or more line correspondences, or by a nonlinear algorithm using three or more line correspondences, where the line correspondences are either given or derived from point correspondences. Then, the translation vector is obtained by solving a set of linear equations based on three or more line correspondences, or two or more point correspondences. Eight 2-D to 3-D line correspondences or six 2-D to 3-D point correspondences are needed for the linear approach; three 2-D to 3-D line or point correspondences for the nonlinear approach. Good results can be obtained in the presence of noise if more than the minimum required number of correspondences are used. > We propose a feature, the Histogram of Oriented Normal Vectors (HONV), designed specifically to capture local geometric characteristics for object recognition with a depth sensor. Through our derivation, the normal vector orientation represented as an ordered pair of azimuthal angle and zenith angle can be easily computed from the gradients of the depth image. We form the HONV as a concatenation of local histograms of azimuthal angle and zenith angle. Since the HONV is inherently the local distribution of the tangent plane orientation of an object surface, we use it as a feature for object detection classification tasks. The object detection experiments on the standard RGB-D dataset [1] and a self-collected Chair-D dataset show that the HONV significantly outperforms traditional features such as HOG on the depth image and HOG on the intensity image, with an improvement of 11.6 in average precision. For object classification, the HONV achieved 5.0 improvement over state-of-the-art approaches. We propose using global orientation from inertial measurements, and the bias it induces on the shape of objects populating the scene, to inform visual three-dimensional reconstruction. We test the effect of using the resulting prior in-depth prediction from a single image, where the normal vectors to surfaces of objects of certain classes tend to align with gravity or be orthogonal to it. Adding such a prior to baseline methods for monocular depth prediction yields improvements beyond the state-of-the-art and illustrates the power of gravity as a supervisory signal. This paper presents a new method that permits to estimate, in the viewer coordinate system, the spatial attitude of an articulated object from a single perspective image. Its principle is based on the interpretation of some image lines as the perspective projection of linear ridges of the object model, and on an iterative search of the model attitude consistent with these projections. The presented method doesn't locate separately the different parts of the object by using for each of them a technics devoted to the localization of rigid object but computes a global attitude which respects the mechanical articulations of the objet. In fact, the geometrical transformations applied to the model to bring it into the correct attitude are obtained in two steps. The first one is devoted to the estimation of the attitude parameters corresponding to a rotation and involves an iterative process. The second step permits by the resolution of a linear system to estimate the translation parameters. The presented experiments correspond to the localization of robot arms from synthetical and real images. The former case permits to appreciate the accuracy of the method since the final result of the pose estimation can be compared with the attitude parameters used to create the synthetical image. The latter case presents an experiment made in an industrial environment and involves the estimation of twelve paramaters since the observed robot arm owns six inner degrees of freedom. The presented method can be useful in some operation driven by remote control. Multi-view structure from motion (SfM) estimates the position and orientation of pictures in a common 3D coordinate frame. When views are treated incrementally, this external calibration can be subject to drift, contrary to global methods that distribute residual errors evenly. We propose a new global calibration approach based on the fusion of relative motions between image pairs. We improve an existing method for robustly computing global rotations. We present an efficient a contrario trifocal tensor estimation method, from which stable and precise translation directions can be extracted. We also define an efficient translation registration method that recovers accurate camera positions. These components are combined into an original SfM pipeline. Our experiments show that, on most datasets, it outperforms in accuracy other existing incremental and global pipelines. It also achieves strikingly good running times: it is about 20 times faster than the other global method we could compare to, and as fast as the best incremental method. More importantly, it features better scalability properties. This paper presents a novel method for learning object manipulation such as rotating an object or placing one object on another. In this method, motions are learned using reference-point-dependent probabilistic models, which can be used for the generation and recognition of motions. The method estimates (i) the reference point, (ii) the intrinsic coordinate system type, which is the type of coordinate system intrinsic to a motion, and (iii) the probabilistic model parameters of the motion that is considered in the intrinsic coordinate system. Motion trajectories are modeled by a hidden Markov model (HMM), and an HMM-based method using static and dynamic features is used for trajectory generation. The method was evaluated in physical experiments in terms of motion generation and recognition. In the experiments, users demonstrated the manipulation of puppets and toys so that the motions could be learned. A recognition accuracy of 90 was obtained for a test set of motions performed by three subjects. Furthe... The control task of tracking a reference pointing direction (the attitude about the pointing direction is irrelevant) while obtaining a desired angular velocity (PDAV) around the pointing direction using geometric techniques is addressed here. Existing geometric controllers developed on the two-sphere only address the tracking of a reference pointing direction while driving the angular velocity about the pointing direction to zero. In this paper a tracking controller on the two-sphere, able to address the PDAV control task, is developed globally in a geometric frame work, to avoid problems related to other attitude representations such as unwinding (quaternions) or singularities (Euler angles). An attitude error function is constructed resulting in a control system with desired tracking performance for rotational maneuvers with large initial attitude angular velocity errors and the ability to negotiate bounded modeling inaccuracies. The tracking ability of the developed control system is evaluated by comparing its performance with an existing geometric controller on the two-sphere and by numerical simulations, showing improved performance for large initial attitude errors, smooth transitions between desired angular velocities and the ability to negotiate bounded modeling inaccuracies. Ten different feature vectors are tested in a gesture recognition task which utilizes 3D data gathered in real-time from stereo video cameras, and HMMs for learning and recognition of gestures. Results indicate velocity features are superior to positional features, and partial rotational invariance is sufficient for good performance.