Disparity Gradients and Depth Scaling

The binocular perception of shape and depth relations between objects can change considerably if the viewing direction is changed only by a small angle. We explored this effect psychophysically and found a strong depth reduction effect for large disparity gradients. The effect is found to be strongest for horizontally oriented stimuli, and stronger for line stimuli than for points. This depth scaling effect is discussed in a computational framework of stereo based on a Baysian approach which allows integration of information from different types of matching primitives weighted according to their robustness.

Affine Matching with Bounded Sensor Error: A Study of Geometric Hashing and Alignment

Affine transformations are often used in recognition systems, to approximate the effects of perspective projection. The underlying mathematics is for exact feature data, with no positional uncertainty. In practice, heuristics are added to handle uncertainty. We provide a precise analysis of affine point matching, obtaining an expression for the range of affine-invariant values consistent with bounded uncertainty. This analysis reveals that the range of affine-invariant values depends on the actual $x$-$y$-positions of the features, i.e. with uncertainty, affine representations are not invariant with respect to the Cartesian coordinate system. We analyze the effect of this on geometric hashing and alignment recognition methods.

Template Matching: Matched Spatial Filters and Beyond

Template matching by means of cross-correlation is common practice in pattern recognition. However, its sensitivity to deformations of the pattern and the broad and unsharp peaks it produces are significant drawbacks. This paper reviews some results on how these shortcomings can be removed. Several techniques (Matched Spatial Filters, Synthetic Discriminant Functions, Principal Components Projections and Reconstruction Residuals) are reviewed and compared on a common task: locating eyes in a database of faces. New variants are also proposed and compared: least squares Discriminant Functions and the combined use of projections on eigenfunctions and the corresponding reconstruction residuals. Finally, approximation networks are introduced in an attempt to improve filter design by the introduction of nonlinearity.

Direct Estimation of Motion and Extended Scene Structure from a Moving Stereo Rig

We describe a new method for motion estimation and 3D reconstruction from stereo image sequences obtained by a stereo rig moving through a rigid world. We show that given two stereo pairs one can compute the motion of the stereo rig directly from the image derivatives (spatial and temporal). Correspondences are not required. One can then use the images from both pairs combined to compute a dense depth map. The motion estimates between stereo pairs enable us to combine depth maps from all the pairs in the sequence to form an extended scene reconstruction and we show results from a real image sequence. The motion computation is a linear least squares computation using all the pixels in the image. Areas with little or no contrast are implicitly weighted less so one does not have to explicitly apply a confidence measure.

Structure from Stereo and Motion

Stereopsis and motion parallax are two methods for recovering three dimensional shape. Theoretical analyses of each method show that neither alone can recover rigid 3D shapes correctly unless other information, such as perspective, is included. The solutions for recovering rigid structure from motion have a reflection ambiguity; the depth scale of the stereoscopic solution will not be known unless the fixation distance is specified in units of interpupil separation. (Hence the configuration will appear distorted.) However, the correct configuration and the disposition of a rigid 3D shape can be recovered if stereopsis and motion are integrated, for then a unique solution follows from a set of linear equations. The correct interpretation requires only three points and two stereo views.

Fast Contour Matching Using Approximate Earth Mover's Distance

Weighted graph matching is a good way to align a pair of shapes represented by a set of descriptive local features; the set of correspondences produced by the minimum cost of matching features from one shape to the features of the other often reveals how similar the two shapes are. However, due to the complexity of computing the exact minimum cost matching, previous algorithms could only run efficiently when using a limited number of features per shape, and could not scale to perform retrievals from large databases. We present a contour matching algorithm that quickly computes the minimum weight matching between sets of descriptive local features using a recently introduced low-distortion embedding of the Earth Mover's Distance (EMD) into a normed space. Given a novel embedded contour, the nearest neighbors in a database of embedded contours are retrieved in sublinear time via approximate nearest neighbors search. We demonstrate our shape matching method on databases of 10,000 images of human figures and 60,000 images of handwritten digits.

Robust Photo-topography by Fusing Shape-from-Shading and Stereo

Methods for fusing two computer vision methods are discussed and several example algorithms are presented to illustrate the variational method of fusing algorithms. The example algorithms seek to determine planet topography given two images taken from two different locations with two different lighting conditions. The algorithms each employ assingle cost function that combines the computer vision methods of shape-from-shading and stereo in different ways. The algorithms are closely coupled and take into account all the constraints of the photo-topography problem. The algorithms are run on four synthetic test image sets of varying difficulty.

On Interpreting Stereo Disparity

The problems under consideration center around the interpretation of binocular stereo disparity. In particular, the goal is to establish a set of mappings from stereo disparity to corresponding three-dimensional scene geometry. An analysis has been developed that shows how disparity information can be interpreted in terms of three-dimensional scene properties, such as surface depth, discontinuities, and orientation. These theoretical developments have been embodied in a set of computer algorithms for the recovery of scene geometry from input stereo disparity. The results of applying these algorithms to several disparity maps are presented. Comparisons are made to the interpretation of stereo disparity by biological systems.

Improving ICP with Easy Implementation for Free Form Surface Matching

Liu, Yonghuai. Improving ICP with Easy Implementation for Free Form Surface Matching. Pattern Recognition, vol. 37, no. 2, pp. 211-226, 2004.

Automatic 3d free form shape matching using the graduated assignment algorithm.

Liu, Yonghuai. Automatic 3d free form shape matching using the graduated assignment algorithm. Pattern Recognition, vol. 38, no. 10, pp. 1615-1631, 2005.

Multi-scale 3D Scene Flow from Binocular Stereo Sequences

Scene flow methods estimate the three-dimensional motion field for points in the world, using multi-camera video data. Such methods combine multi-view reconstruction with motion estimation approaches. This paper describes an alternative formulation for dense scene flow estimation that provides convincing results using only two cameras by fusing stereo and optical flow estimation into a single coherent framework. To handle the aperture problems inherent in the estimation task, a multi-scale method along with a novel adaptive smoothing technique is used to gain a regularized solution. This combined approach both preserves discontinuities and prevents over-regularization-two problems commonly associated with basic multi-scale approaches. Internally, the framework generates probability distributions for optical flow and disparity. Taking into account the uncertainty in the intermediate stages allows for more reliable estimation of the 3D scene flow than standard stereo and optical flow methods allow. Experiments with synthetic and real test data demonstrate the effectiveness of the approach.

Modal Matching for Correspondence and Recognition

Modal matching is a new method for establishing correspondences and computing canonical descriptions. The method is based on the idea of describing objects in terms of generalized symmetries, as defined by each object's eigenmodes. The resulting modal description is used for object recognition and categorization, where shape similarities are expressed as the amounts of modal deformation energy needed to align the two objects. In general, modes provide a global-to-local ordering of shape deformation and thus allow for selecting which types of deformations are used in object alignment and comparison. In contrast to previous techniques, which required correspondence to be computed with an initial or prototype shape, modal matching utilizes a new type of finite element formulation that allows for an object's eigenmodes to be computed directly from available image information. This improved formulation provides greater generality and accuracy, and is applicable to data of any dimensionality. Correspondence results with 2-D contour and point feature data are shown, and recognition experiments with 2-D images of hand tools and airplanes are described.

Multi-Scale 3D Scene Flow from Binocular Stereo Sequences

Scene flow methods estimate the three-dimensional motion field for points in the world, using multi-camera video data. Such methods combine multi-view reconstruction with motion estimation. This paper describes an alternative formulation for dense scene flow estimation that provides reliable results using only two cameras by fusing stereo and optical flow estimation into a single coherent framework. Internally, the proposed algorithm generates probability distributions for optical flow and disparity. Taking into account the uncertainty in the intermediate stages allows for more reliable estimation of the 3D scene flow than previous methods allow. To handle the aperture problems inherent in the estimation of optical flow and disparity, a multi-scale method along with a novel region-based technique is used within a regularized solution. This combined approach both preserves discontinuities and prevents over-regularization – two problems commonly associated with the basic multi-scale approaches. Experiments with synthetic and real test data demonstrate the strength of the proposed approach.

Object Matching in Distributed Video Surveillance Systems by LDA-Based Appearance Descriptors

Establishing correspondences among object instances is still challenging in multi-camera surveillance systems, especially when the cameras’ fields of view are non-overlapping. Spatiotemporal constraints can help in solving the correspondence problem but still leave a wide margin of uncertainty. One way to reduce this uncertainty is to use appearance information about the moving objects in the site. In this paper we present the preliminary results of a new method that can capture salient appearance characteristics at each camera node in the network. A Latent Dirichlet Allocation (LDA) model is created and maintained at each node in the camera network. Each object is encoded in terms of the LDA bag-of-words model for appearance. The encoded appearance is then used to establish probable matching across cameras. Preliminary experiments are conducted on a dataset of 20 individuals and comparison against Madden’s I-MCHR is reported.

An Invariant Representation for Matching Trajectories across Uncalibrated Video Streams

We introduce a view-point invariant representation of moving object trajectories that can be used in video database applications. It is assumed that trajectories lie on a surface that can be locally approximated with a plane. Raw trajectory data is first locally approximated with a cubic spline via least squares fitting. For each sampled point of the obtained curve, a projective invariant feature is computed using a small number of points in its neighborhood. The resulting sequence of invariant features computed along the entire trajectory forms the view invariant descriptor of the trajectory itself. Time parametrization has been exploited to compute cross ratios without ambiguity due to point ordering. Similarity between descriptors of different trajectories is measured with a distance that takes into account the statistical properties of the cross ratio, and its symmetry with respect to the point at infinity. In experiments, an overall correct classification rate of about 95% has been obtained on a dataset of 58 trajectories of players in soccer video, and an overall correct classification rate of about 80% has been obtained on matching partial segments of trajectories collected from two overlapping views of outdoor scenes with moving people and cars.