Detecting textured objects using convex hull

In this paper, we present a methodology of locating 3D objects of known shapes from a single gray-scale image, in particular objects with rich textures on the surface. While traditional approaches identify objects by grouping and matching local features, we locate the object in the image using its convex hull, a high level feature not given much attention in the image using literature. A “direct line detection” algorithm is developed to detect line segments directly from the gray-scale image divided in small blocks. Lines are clustered and convex hull of a single or group of clusters is computed and edited to extract the 2D contour of the object. Successful experiments on rectangular boxes and cylinders show the effectiveness of the convex hull approach and its potential usage in industrial applications. Part of the work discussed in this paper was performed when both authors were affiliated with Symbol Technologies.     

Interpreting line drawings of curved objects

In this paper, we study the problem of interpreting line drawings of scenes composed of opaque regular solid objects bounded by piecewise smooth surfaces with no markings or texture on them. It is assumed that the line drawing has been formed by orthographic projection of such a scene under general viewpoint, that the line drawing is error free, and that there are no lines due to shadows or specularities. Our definition implicitly excludes laminae, wires, and the apices of cones.A major component of the interpretation of line drawings is line labelling. By line labelling we mean (a) classification of each image curve as corresponding to either a depth or orientation discontinuity in the scene, and (b) further subclassification of each kind of discontinuity. For a depth discontinuity we determine whether it is a limb—a locus of points on the surface where the line of sight is tangent to the surface—or an occluding edge—a tangent plane discontinuity of the surface. For an orientation discontinuity, we determine whether it corresponds to a convex or concave edge. This paper presents the first mathematically rigorous scheme for labelling line drawings of the class of scenes described. Previous schemes for labelling line drawings of scenes containing curved objects were heuristic, incomplete, and lacked proper mathematical justification.By analyzing the projection of the neighborhoods of different kinds of points on a piecewise smooth surface, we are able to catalog all local labelling possibilities for the different types of junctions in a line drawing. An algorithm is developed which utilizes this catalog to determine all legal labellings of the line drawing. A local minimum complexity rule—at each vertex select those labellings which correspond to the minimum number of faces meeting at the vertex—is used in order to prune highly counter-intuitive interpretations. The labelling scheme was implemented and tested on a number of line drawings. The labellings obtained are few and by and large in accordance with human interpretations.     

On the recognition of curved objects

The problem of determining the identity and pose of occluded objects from noisy data is examined. Previous work has shown that local measurements of the position and surface orientation of small patches of an object's surface may be used in a constrained search process to solve this problem, for the case of rigid polygonal objects using 2-D sensory data, or rigid polyhedral objects using 3-D data. The recognition system is extended to recognize and locate curved objects. The extension is done in two dimensions, and applies to the recognition of 2-D objects from 2-D data, or to the recognition of the 3-D objects in stable positions from 2-D data     

The visual hull concept for silhouette-based image understanding

Many algorithms for both identifying and reconstructing a 3-D object are based on the 2-D silhouettes of the object. In general, identifying a nonconvex object using a silhouette-based approach implies neglecting some features of its surface as identification clues. The same features cannot be reconstructed by volume intersection techniques using multiple silhouettes of the object. This paper addresses the problem of finding which parts of a nonconvex object are relevant for silhouette-based image understanding. For this purpose, the geometric concept of visual hull of a 3-D object is introduced. This is the closest approximation of object S that can be obtained with the volume intersection approach; it is the maximal object silhouette-equivalent to S, i.e., which can be substituted for S without affecting any silhouette. Only the parts of the surface of S that also lie on the surface of the visual hull can be reconstructed or identified using silhouette-based algorithms. The visual hull depends not only on the object but also on the region allowed to the viewpoint. Two main viewing regions result in the external and internal visual hull. In the former case the viewing region is related to the convex hull of S, in the latter it is bounded by S. The internal visual hull also admits an interpretation not related to silhouettes. Algorithms for computing visual hulls are presented and their complexity analyzed. In general, the visual hull of a 3-D planar face object turns out to be bounded by planar and curved patches     

Recognition and localization of objects with curved surfaces

This paper concerns the problem of recognition and localization of three-dimensional objects from range data. Most of the previous approaches suffered from one or both of the following shortcomings: (1) They dealt with single object scenes and/or (2) they dealt with polyhedral objects or objects that were approximated as polyhedra. The work in this paper addresses both of these shortcomings. The input scenes are allowed to contain multiple objects with partial occlusion. The objects are not restricted to polyhedra but are allowed to have a piecewise combination of curved surfaces, namely, spherical, cylindrical, and conical surfaces. This restriction on the types of curved surfaces is not unreasonable since most objects encountered in an industrial environment can be thus modeled. This paper shows how the qualitative classification of the surfaces based on the signs of the mean and Gaussian curvature can be used to come up withdihedral feature junctions as features to be used for recognition and localization. Dihedral feature junctions are robust to occlusion, offer a viewpoint independent modeling technique for the object models, do not require elaborate segmentation, and the feature extraction process is amenable to parallelism. Hough clustering on account of its ease of parallelization is chosen as the constraint propagation/ satisfaction mechanisms. Experimental results are presented using the Connection Machine. The fine-grained architecture of the Connection Machine is shown to be well suited for the recognition/localization technique presented in this paper.     

Online gesture spotting from visual hull data

This paper presents a robust framework for online full-body gesture spotting from visual hull data. Using view-invariant pose features as observations, hidden Markov models (HMMs) are trained for gesture spotting from continuous movement data streams. Two major contributions of this paper are 1) view-invariant pose feature extraction from visual hulls, and 2) a systematic approach to automatically detecting and modeling specific nongesture movement patterns and using their HMMs for outlier rejection in gesture spotting. The experimental results have shown the view-invariance property of the proposed pose features for both training poses and new poses unseen in training, as well as the efficacy of using specific nongesture models for outlier rejection. Using the IXMAS gesture data set, the proposed framework has been extensively tested and the gesture spotting results are superior to those reported on the same data set obtained using existing state-of-the-art gesture spotting methods.     

Shape measurement of curved objects using multiple slit-ray projections

A method for the shape measurement of curved objects has been developed using multiple slit-ray projections and a turntable. The object is placed on a computer-controlled turntable and irradiated by two directed slit-ray projectors. An ITV camera takes a line image of the reflection from the object, and a computer calculates the space coordinates of the object surface. By using multiple projections, the total shape measurement of the object surface is attained accurately.     

Determining pose of 3D objects with curved surfaces

A method is presented for computing the pose of rigid 3D objects with arbitrary curved surfaces. Given an input image and a candidate object model and aspect, the method will verify whether or not the object is present and if so, report pose parameters. The curvature method of Bash and Ullman is used to model points on the object rim, while stereo matching is used for internal edge points. The model allows an object edge-map to be predicted from pose parameters. Pose is computed via an iterative search for the best pose parameters. Heuristics are used so that matching can succeed in the presence of occlusion and artifact and without resetting to use of corresponding salient feature points. Bench tests and simulations show that the method almost always converges to ground truth pose parameters for a variety of objects and for a broad set of starting parameters in the same aspect     

GPU-based parallel construction of compact visual hull meshes

Building a visual hull model from multiple two-dimensional images provides an effective way of understanding the three-dimensional geometries inherent in the images. In this paper, we present a GPU accelerated algorithm for volumetric visual hull reconstruction that aims to harness the full compute power of the many-core processor. From a set of binary silhouette images with respective camera parameters, our parallel algorithm directly outputs the triangular mesh of the resulting visual hull in the indexed face set format for a compact mesh representation. Unlike previous approaches, the presented method extracts a smooth silhouette contour on the fly from each binary image, which markedly reduces the bumpy artifacts on the visual hull surface due to a simple binary in/out classification. In addition, it applies several optimization techniques that allow an efficient CUDA implementation. We also demonstrate that the compact mesh construction scheme can easily be modified for also producing a time- and space-efficient GPU implementation of the marching cubes algorithm.     

Computing stable poses of piecewise smooth objects

When a three dimensional object is known to be lying on a planar surface, its pose is restricted from six to three degrees of freedom. Computer vision algorithms can exploit the few stable poses of modeled objects to simplify scene interpretation and more accurately determine object location. This paper presents necessary and sufficient conditions for the pose of a piecewise smooth curved three-dimensional object to be stable. For objects whose surfaces are represented by implicit algebraic equations, these conditions can be expressed as systems of polynomial equations that are readily solved by homotopy continuation. Examples from the implemented algorithm are presented.     

3D reconstruction of complex curved objects from line drawings

An active research topic in computer vision and graphics is developing algorithms that can reconstruct the 3D surface of curved objects from line drawings. There are a number of algorithms have been dedicated to solve this problem, but they can't solve this problem when the geometric structure of a curved object becomes complex. This paper proposes a novel approach to reconstructing a complex curved 3D object from single 2D line drawings. Our approach has three steps:(1) decomposing a complex line drawing into several simpler line drawings and transforming them into polyhedron;(2) reconstructing the 3D wireframe of curved object from these simpler line drawings and generating the curved faces;(3) combining the 3D objects into the complete objects. A number of examples are given to demonstrate the ability of our approach to successfully perform reconstruction of curved objects which are more complex than previous methods.     

Computing exact aspect graphs of curved objects: Algebraic surfaces

This article presents an algorithm for computing the exact aspect graph of an opaque solid bounded by a smooth algebraic surface. Orthographic projection is assumed. The algorithm is based on a catalog of visual events available from singularity theory. It uses curve tracing, cell decomposition, homotopy continuation, and ray tracing to construct the regions of the view sphere delineated by visual-event curves. The algorithm has been fully implemented, and examples are presented.     

Computing exact aspect graphs of curved objects: Solids of revolution

This paper introduces a new approach to computing the exact orthographic aspect graph of curved objects. Curves corresponding to various visual events partition the view sphere into regions where the image structure is stable. A catalog of these events for piecewise-smooth objects is available from singularity theory. For a solid of revolution whose generator is an algebraic curve, each visual event is characterized by a system of polynomial equations whose roots can be computed by continuation methods. Within each region, the stable image structure is characterized by a variation of cylindrical algebraic decomposition and ray tracing. This approach has been implemented and several examples are presented.     

On recognizing and positioning curved 3-D objects from imagecontours

An approach for explicitly relating the shape of image contours to models of curved three-dimensional objects is presented. This relationship is used for object recognition and positioning. Object models consist of collections of parametric surface patches and their intersection curves; this includes nearly all representations used in computer-aided geometric design and computer vision. The image contours considered are the projections of surface discontinuities and occluding contours. Elimination theory provides a method for constructing the implicit equation of these contours for an object observed under orthographic or perspective projection. This equation is parameterized by the object's position and orientation with respect to the observer. Determining these parameters is reduced to a fitting problem between the theoretical contour and the observed data points. The proposed approach readily extends to parameterized models. It has been implemented for a simple world composed of various surfaces of revolution and tested on several real images     

A rich discrete labeling scheme for line drawings of curved objects

We present a discrete labeling scheme for line drawings of curved objects which can be seen as an information-rich extension of the classic line-labeling scheme in which lines are classified as convex, concave, occluding or extremal. New labels are introduced to distinguish between curved and planar surface-patches, to identify orthogonal edges and to indicate gradient directions of planar surface-patches.     

Learning separate visual representations of independently rotating objects

Individual cells that respond preferentially to particular objects have been found in the ventral visual pathway. How the brain is able to develop neurons that exhibit these object selective responses poses a significant challenge for computational models of object recognition. Typically, many objects make up a complex natural scene and are never presented in isolation. Nonetheless, the visual system is able to build invariant object selective responses. In this paper, we present a model of the ventral visual stream, VisNet, which can solve the problem of learning object selective representations even when multiple objects are always present during training. Past research with the VisNet model has shown that the network can operate successfully in a similar training paradigm, but only when training comprises many different object pairs. Numerous pairings are required for statistical decoupling between objects. In this research, we show for the first time that VisNet is capable of utilizing the statistics inherent in independent rotation to form object selective representations when training with just two objects, always presented together. Crucially, our results show that in a dependent rotation paradigm, the model fails to build object selective representations and responds as if the two objects are in fact one. If the objects begin to rotate independently, the network forms representations for each object separately.     

Incorporating object-centered sampling and Delaunay tetrahedrization for visual hull reconstruction

In this paper we present a novel shape from silhouette algorithm. For an object to be modeled, the algorithm first computes a cloud of points located on a pencil of rays and distributed evenly on the visual hull surface, inside and outside the visual hull. Then Delaunay tetrahedrization is applied to the point cloud to partition its convex hull into a set of tetrahedrons. Finally, outlier tetrahedrons are removed by tetrahedron peeling, and a mesh model of the visual hull is extracted. The algorithm is robust, free from discretization artifacts, and produces a mesh model composed of well-shaped triangles.