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
1489924732 2094963281
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. In moving camera videos, motion segmentation is commonly performed using the image plane motion of pixels, or optical flow. However, objects that are at different depths from the camera can exhibit different optical flows even if they share the same real-world motion. This can cause a depth-dependent segmentation of the scene. Our goal is to develop a segmentation algorithm that clusters pixels that have similar real-world motion irrespective of their depth in the scene. Our solution uses optical flow orientations instead of the complete vectors and exploits the well-known property that under camera translation, optical flow orientations are independent of object depth. We introduce a probabilistic model that automatically estimates the number of observed independent motions and results in a labeling that is consistent with real-world motion in the scene. The result of our system is that static objects are correctly identified as one segment, even if they are at different depths. Color features and information from previous frames in the video sequence are used to correct occasional errors due to the orientation-based segmentation. We present results on more than thirty videos from different benchmarks. The system is particularly robust on complex background scenes containing objects at significantly different depths. 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. Recently, there has been interest in formulating various geometric problems in Computer Vision as L optimization problems. The advantage of this approach is that under L norm, such problems typically have a single minimum, and may be efficiently solved using Second-Order Cone Programming (SOCP). This paper shows that such techniques may be used effectively on the problem of determining the track of a camera given observations of features in the environment. The approach to this problem involves two steps: determination of the orientation of the camera by estimation of relative orientation between pairs of views, followed by determination of the translation of the camera. This paper focusses on the second step, that of determining the motion of the camera. It is shown that it may be solved effectively by using SOCP to reconcile translation estimates obtained for pairs or triples of views. In addition, it is observed that the individual translation estimates are not known with equal certainty in all directions. To account for this anisotropy in uncertainty, we introduce the use of covariances into the L optimization framework. One of the major drawbacks of orthogonal wavelet transforms is their lack of translation invariance: the content of wavelet subbands is unstable under translations of the input signal. Wavelet transforms are also unstable with respect to dilations of the input signal and, in two dimensions, rotations of the input signal. The authors formalize these problems by defining a type of translation invariance called shiftability. In the spatial domain, shiftability corresponds to a lack of aliasing; thus, the conditions under which the property holds are specified by the sampling theorem. Shiftability may also be applied in the context of other domains, particularly orientation and scale. Jointly shiftable transforms that are simultaneously shiftable in more than one domain are explored. Two examples of jointly shiftable transforms are designed and implemented: a 1-D transform that is jointly shiftable in position and scale, and a 2-D transform that is jointly shiftable in position and orientation. The usefulness of these image representations for scale-space analysis, stereo disparity measurement, and image enhancement is demonstrated. > Many systems for recording human movement need some reference from beacons near the subject, such as video cameras. Our goal is to measure human kinematics with sensors that are placed on the segments of interest. This way, experiments in which human movement is recorded are not restricted to a lab. Our inertial sensor-unit consists of a little box with three miniature gyroscopes (Murata ENC05E) and three linear accelerometers (AD xl05) that measure 3D angular velocity and linear acceleration, respectively. Both the gyroscope and accelerometer signals contain information about the orientation of the sensor. The sensor orientation can be obtained by integration of the angular velocity signals obtained from the gyroscopes [1]. This operation introduces drift in the estimated orientation. Accelerometers do not only measure the acceleration of the sensor, but also the gravitational vector. This gravitational component not only has a bigger magnitude for many human movements but also always points downwards. This knowledge can be used to make an estimation of the tilt. The tilt is the angle between the sensor axes and the vertical. This tilt estimation is not very precise but does not suffer from drift. The abstract describes a way to fuse both sensors (gyroscopes and accelerometers) to obtain an estimate of the orientation that is both accurate and is limited in integration drift. This paper discusses how local measurements of three-dimensional positions and surface normals (recorded by a set of tactile sensors, or by three-dimensional range sensors), may be used to identify and locate objects from among a set of known objects. The objects are modeled as polyhedra having up to six degrees of freedom relative to the sensors. We show that inconsistent hypotheses about pairings between sensed points and object surfaces can be discarded efficiently by using local constraints on distances between faces, angles between face normals, and angles (relative to the surface normals) of vectors between sensed points. We show by simulation and by mathematical bounds that the number of hypotheses consistent with these constraints is small We also show how to recover the position and orientation of the object from the sensory data. The algorithm's performance on data obtained from a triangulation range sensor is illustrated. Multiresolution representations are effective for analyzing the information content of images. The properties of the operator which approximates a signal at a given resolution were studied. It is shown that the difference of information between the approximation of a signal at the resolutions 2 sup j+1 and 2 sup j (where j is an integer) can be extracted by decomposing this signal on a wavelet orthonormal basis of L sup 2 (R sup n ), the vector space of measurable, square-integrable n-dimensional functions. In L sup 2 (R), a wavelet orthonormal basis is a family of functions which is built by dilating and translating a unique function psi (x). This decomposition defines an orthogonal multiresolution representation called a wavelet representation. It is computed with a pyramidal algorithm based on convolutions with quadrature mirror filters. Wavelet representation lies between the spatial and Fourier domains. For images, the wavelet representation differentiates several spatial orientations. The application of this representation to data compression in image coding, texture discrimination and fractal analysis is discussed. > We present an approach to recognition of complex objects in cluttered 3-D scenes that does not require feature extraction or segmentation. Our object representation comprises descriptive images associated with each oriented point on the surface of an object. Using a single point basis constructed from an oriented point, the position of other points on the surface of the object can be described by two parameters. The accumulation of these parameters for many points on the surface of the object results in an image at each oriented point. These images, localized descriptions of the global shape of the object, are invariant to rigid transformations. Through correlation of images, point correspondences between a model and scene data are established and then grouped using geometric consistency. The effectiveness of our algorithm is demonstrated with results showing recognition of complex objects in cluttered scenes with occlusion. We introduce tensor field neural networks, which are locally equivariant to 3D rotations, translations, and permutations of points at every layer. 3D rotation equivariance removes the need for data augmentation to identify features in arbitrary orientations. Our network uses filters built from spherical harmonics; due to the mathematical consequences of this filter choice, each layer accepts as input (and guarantees as output) scalars, vectors, and higher-order tensors, in the geometric sense of these terms. We demonstrate the capabilities of tensor field networks with tasks in geometry, physics, and chemistry. 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. A novel technique called photometric stereo is introduced. The idea of photometric stereo is to vary the direction of incident illumination between successive images, while holding the viewing direction constant. It is shown that this provides sufficient information to determine surface orientation at each image point. Since the imaging geometry is not changed, the correspondence between image points is known a priori. The technique is photometric because it uses the radiance values recorded at a single image location, in successive views, rather than the relative positions of displaced features. Photometric stereo is used in computer-based image understanding. It can be applied in two ways. First, it is a general technique for deter-mining surface orientation at each image point. Second, it is a technique for determining object points that have a particular surface orientation. These applications are illustrated using synthesized examples. The observation of objects located in inaccessible regions is a recurring challenge in a wide variety of important applications. Recent work has shown that using rare and expensive optical setups, indirect diffuse light reflections can be used to reconstruct objects and two-dimensional (2D) patterns around a corner. Here we show that occluded objects can be tracked in real time using much simpler means, namely a standard 2D camera and a laser pointer. Our method fundamentally differs from previous solutions by approaching the problem in an analysis-by-synthesis sense. By repeatedly simulating light transport through the scene, we determine the set of object parameters that most closely fits the measured intensity distribution. We experimentally demonstrate that this approach is capable of following the translation of unknown objects, and translation and orientation of a known object, in real time. In this paper, we propose a new approach for heartbeat classification based on a combination of morphological and dynamic features. Wavelet transform and independent component analysis (ICA) are applied separately to each heartbeat to extract morphological features. In addition, RR interval information is computed to provide dynamic features. These two different types of features are concatenated and a support vector machine classifier is utilized for the classification of heartbeats into one of 16 classes. The procedure is independently applied to the data from two ECG leads and the two decisions are fused for the final classification decision. The proposed method is validated on the baseline MIT-BIH arrhythmia database and it yields an overall accuracy (i.e., the percentage of heartbeats correctly classified) of 99.3 (99.7 with 2.4 rejection) in the “class-oriented” evaluation and an accuracy of 86.4 in the “subject-oriented” evaluation, comparable to the state-of-the-art results for automatic heartbeat classification. Representing documents by vectors that are independent of language enhances machine translation and multilingual text categorization. We use discriminative training to create a projection of documents from multiple languages into a single translingual vector space. We explore two variants to create these projections: Oriented Principal Component Analysis (OPCA) and Coupled Probabilistic Latent Semantic Analysis (CPLSA). Both of these variants start with a basic model of documents (PCA and PLSA). Each model is then made discriminative by encouraging comparable document pairs to have similar vector representations. We evaluate these algorithms on two tasks: parallel document retrieval for Wikipedia and Europarl documents, and cross-lingual text classification on Reuters. The two discriminative variants, OPCA and CPLSA, significantly outperform their corresponding baselines. The largest differences in performance are observed on the task of retrieval when the documents are only comparable and not parallel. The OPCA method is shown to perform best. Automated metrics such as BLEU are widely used in the machine translation literature. They have also been used recently in the dialogue community for evaluating dialogue response generation. However, previous work in dialogue response generation has shown that these metrics do not correlate strongly with human judgment in the non task-oriented dialogue setting. Task-oriented dialogue responses are expressed on narrower domains and exhibit lower diversity. It is thus reasonable to think that these automated metrics would correlate well with human judgment in the task-oriented setting where the generation task consists of translating dialogue acts into a sentence. We conduct an empirical study to confirm whether this is the case. Our findings indicate that these automated metrics have stronger correlation with human judgments in the task-oriented setting compared to what has been observed in the non task-oriented setting. We also observe that these metrics correlate even better for datasets which provide multiple ground truth reference sentences. In addition, we show that some of the currently available corpora for task-oriented language generation can be solved with simple models and advocate for more challenging datasets. 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. An experiment is presented comparing the effects of various virtual travel techniques in an immersive virtual environment (VE) on the spatial orientation of users. The experiment was designed and implemented in the context of a formal framework for the design and evaluation of VE travel techniques. Subjects traveled through virtual corridors, noting the location of objects along the way, and were asked to point in the direction of one of these objects when the end of the corridor was reached. Results indicate that virtual travel techniques, in which users do not physically translate their bodies, can allow the maintenance of a user's spatial orientation as measured by a pointing task. The experiment also replicates an earlier result, showing that path dimension significantly affects user performance. Finally, the strategies used by subjects to perform the task were shown to be significant, indicating that performance depends not only on the technique, environment, and task, but also on the sophistication of the user. Abstract This paper mathematically analyzes and proposes new solutions for the problem of estimating the camera 3D location and orientation ( pose determination ) from a matched set of 3D model and 2D image landmark features. Least-squares techniques for line tokens, which minimize both rotation and translation simultaneously, are developed and shown to be far superior to the earlier techniques which solved for rotation first and then translation. However, least-squares techniques fail catastrophically when outliers (or gross errors) are present in the match data. Outliers arise frequently due to incorrect correspondences or gross errors in the 3D model. Robust techniques for pose determination are developed to handle data contaminated by fewer than 50.0 outliers. Finally, the sensitivity of pose determination to incorrect estimates of camera parameters is analyzed. It is shown that for small field of view systems, offsets in the image center do not significantly affect the location of the camera in a world coordinate system. Errors in the focal length significantly affect only the component of translation along the optical axis in the pose computation. 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. >