Instance-based object recognition in 3D point clouds using discriminative shape primitives

3D local shapes are a critical cue for object recognition in 3D point clouds. This paper presents an instance-based 3D object recognition method via informative and discriminative shape primitives. We propose a shape primitive model that measures geometrical informativity and discriminativity of 3D local shapes of an object. Discriminative shape primitives of the object are extracted automatically by model parameter optimization. We achieve object recognition from 2.5/3D scenes via shape primitive classification and recover the 3D poses of the identified objects simultaneously. The effectiveness and the robustness of the proposed method were verified on popular instance-based 3D object recognition datasets. The experimental results show that the proposed method outperforms some existing instance-based 3D object recognition pipelines in the presence of noise, varying resolutions, clutter and occlusion.     

Animation through space and time based on a space deformation model

To animate deformable objects through time and space, a new technique that will be referred to as DOGMA is proposed here. It is well suited to animation for both interactive design and real-time visualization. The concept of animation primitives based on an extension to animation of the space deformation model is introduced. Animation primitives can be added to any geometrical modeller because they are independent of the underlying geometrical model of the animated objects. It encapsulates animation through space and time under a unique formalism. A local control of deformations both through space and time is easily specified. A direct manipulation of objects is provided. At any time, animated objects are continuously computed from their corresponding animation primitives. This dispenses with the necessity for major storage of the interpolation process. A fully interactive system offers an interactive environment which enables the user to animate deformable objects in real time.     

A structural model for shape recognition using neural nets

Shape representation and recognition is an important topic in many applications of computer vision and artificial intelligence, including character recognition, pattern recognition, machine monitoring, robot manipulation and production part recognition. In this paper, a structural model based on boundary information is proposed to describe the silhouette of planar objects (especially machined parts). The structural model describes objects by a set of primitives, each of which is represented by three geometric features: its length, curvature, and relative orientation. This representation scheme not only compresses the data, but also provides a compact and meaningful form to facilitate further recognition operations. Based on this model, the object recognition is accomplished by using a multilayered feedforward neural network. The proposed model is transformation invariant, which offers the necessary flexibility for real-time implementation in automated manufacturing systems. In addition, the numerical results for a set of ten reference shapes indicate that the matching engine can achieve very high success rates using short recognition times.     

NURBS-based free-form deformations

Since the advent of computer-based geometric modeling, designers have tried to develop modeling and deformation tools that allow users to emulate the ease with which sculptors work with clay. T.W. Sederberg and S.R. Parry (1986) demonstrated the application of free-form deformations. FFDs let the user conceptually embed an object in a clear pliable solid and apply deformations to the solid, which then carry through to the encased object. We describe a technique that logically extends current FFDs by basing them on nonuniform rational B-splines. The resulting NURBS-based FFDs (NFFDs) offer flexibility and control not achieved in prior implementations. We conclude by describing a straightforward combination of this technique with global and local deformations of solid primitives used to animate a lifelike surface model of the human leg     

Discovery of Intrinsic Primitives on Triangle Meshes

The discovery of meaningful parts of a shape is required for many geometry processing applications, such as parameterization, shape correspondence, and animation. It is natural to consider primitives such as spheres, cylinders and cones as the building blocks of shapes, and thus to discover parts by fitting such primitives to a given surface. This approach, however, will break down if primitive parts have undergone almost‐isometric deformations, as is the case, for example, for articulated human models. We suggest that parts can be discovered instead by finding intrinsic primitives, which we define as parts that posses an approximate intrinsic symmetry. We employ the recently‐developed method of computing discrete approximate Killing vector fields (AKVFs) to discover intrinsic primitives by investigating the relationship between the AKVFs of a composite object and the AKVFs of its parts. We show how to leverage this relationship with a standard clustering method to extract k intrinsic primitives and remaining asymmetric parts of a shape for a given k. We demonstrate the value of this approach for identifying the prominent symmetry generators of the parts of a given shape. Additionally, we show how our method can be modified slightly to segment an entire surface without marking asymmetric connecting regions and compare this approach to state‐of‐the‐art methods using the Princeton Segmentation Benchmark.     

Radial Supershapes for Solid Modeling

In the previous work, an efficient method has been proposed to represent solid objects as multiple combinations of globally deformed supershapes. In this paper, this framework is applied with a new supershape implicit function that is based on the notion of radial distance and results are presented on realistic models composed of hundreds of hierarchically globally deformed supershapes. An implicit equation with guaranteed differential properties is obtained by simple combinations of the primitives' implicit representations using R-function theory. The surface corresponding to the zero-set of the implicit equation is efficiently and directly polygonized using the primitives' parametric forms. Moreover, hierarchical global deformations are considered to increase the range of shapes that can be modeled. The potential of the approach is illustrated by representing complex models composed of several hundreds of primitives inspired from CAD models of mechanical parts.     

Recognition of shapes by editing their shock graphs

This paper presents a novel framework for the recognition of objects based on their silhouettes. The main idea is to measure the distance between two shapes as the minimum extent of deformation necessary for one shape to match the other. Since the space of deformations is very high-dimensional, three steps are taken to make the search practical: 1) define an equivalence class for shapes based on shock-graph topology, 2) define an equivalence class for deformation paths based on shock-graph transitions, and 3) avoid complexity-increasing deformation paths by moving toward shock-graph degeneracy. Despite these steps, which tremendously reduce the search requirement, there still remain numerous deformation paths to consider. To that end, we employ an edit-distance algorithm for shock graphs that finds the optimal deformation path in polynomial time. The proposed approach gives intuitive correspondences for a variety of shapes and is robust in the presence of a wide range of visual transformations. The recognition rates on two distinct databases of 99 and 216 shapes each indicate highly successful within category matches (100 percent in top three matches), which render the framework potentially usable in a range of shape-based recognition applications.     

Silhouette-based isolated object recognition through curvaturescale space

A complete, fast and practical isolated object recognition system has been developed which is very robust with respect to scale, position and orientation changes of the objects as well as noise and local deformations of shape (due to perspective projection, segmentation errors and non-rigid material used in some objects). The system has been tested on a wide variety of three-dimensional objects with different shapes and material and surface properties. A light-box setup is used to obtain silhouette images which are segmented to obtain the physical boundaries of the objects which are classified as either convex or concave. Convex curves are recognized using their four high-scale curvature extrema points. Curvature scale space (CSS) representations are computed for concave curves. The CSS representation is a multi-scale organization of the natural, invariant features of a curve (curvature zero-crossings or extrema) and useful for very reliable recognition of the correct model since it places no constraints on the shape of objects. A three-stage, coarse-to-fine matching algorithm prunes the search space in stage one by applying the CSS aspect ratio test. The maxima of contours in CSS representations of the surviving models are used for fast CSS matching in stage two. Finally, stage three verifies the best match and resolves any ambiguities by determining the distance between the image and model curves. Transformation parameter optimization is then used to find the best fit of the input object to the correct model     

Boolean operations with implicit and parametric representation of primitives using R-functions

We present a new and efficient algorithm to accurately polygonize an implicit surface generated by multiple Boolean operations with globally deformed primitives. Our algorithm is special in the sense that it can be applied to objects with both an implicit and a parametric representation, such as superquadrics, supershapes, and Dupin cyclides. The input is a constructive solid geometry tree (CSG tree) that contains the Boolean operations, the parameters of the primitives, and the global deformations. At each node of the CSG tree, the implicit formulations of the subtrees are used to quickly determine the parts to be transmitted to the parent node, while the primitives' parametric definition are used to refine an intermediary mesh around the intersection curves. The output is both an implicit equation and a mesh representing its solution. For the resulting object, an implicit equation with guaranteed differential properties is obtained by simple combinations of the primitives' implicit equations using R-functions. Depending on the chosen R-function, this equation is continuous and can be differentiable everywhere. The primitives' parametric representations are used to directly polygonize the resulting surface by generating vertices that belong exactly to the zero-set of the resulting implicit equation. The proposed approach has many potential applications, ranging from mechanical engineering to shape recognition and data compression. Examples of complex objects are presented and commented on to show the potential of our approach for shape modeling.     

Efficient Path-Space Differentiable Volume Rendering With Respect To Shapes

Differentiable rendering of translucent objects with respect to their shapes has been a long-standing problem. State-of-the-art methods require detecting object silhouettes or specifying change rates inside translucent objects—both of which can be expensive for translucent objects with complex shapes. In this paper, we address this problem for translucent objects with no refractive or reflective boundaries. By reparameterizing interior components of differential path integrals, our new formulation does not require change rates to be specified in the interior of objects. Further, we introduce new Monte Carlo estimators based on this formulation that do not require explicit detection of object silhouettes.     

Shape similarity measure based on correspondence of visual parts

A cognitively motivated similarity measure is presented and its properties are analyzed with respect to retrieval of similar objects in image databases of silhouettes of 2D objects. To reduce influence of digitization noise, as well as segmentation errors, the shapes are simplified by a novel process of digital curve evolution. To compute our similarity measure, we first establish the best possible correspondence of visual parts (without explicitly computing the visual parts). Then, the similarity between corresponding parts is computed and aggregated. We applied our similarity measure to shape matching of object contours in various image databases and compared it to well-known approaches in the literature. The experimental results justify that our shape matching procedure gives an intuitive shape correspondence and is stable with respect to noise distortions.     

Actions as space-time shapes

Human action in video sequences can be seen as silhouettes of a moving torso and protruding limbs undergoing articulated motion. We regard human actions as three-dimensional shapes induced by the silhouettes in the space-time volume. We adopt a recent approach for analyzing 2D shapes and generalize it to deal with volumetric space-time action shapes. Our method utilizes properties of the solution to the Poisson equation to extract space-time features such as local space-time saliency, action dynamics, shape structure and orientation. We show that these features are useful for action recognition, detection and clustering. The method is fast, does not require video alignment and is applicable in (but not limited to) many scenarios where the background is known. Moreover, we demonstrate the robustness of our method to partial occlusions, non-rigid deformations, significant changes in scale and viewpoint, high irregularities in the performance of an action, and low quality video.     

3-D shape recovery using distributed aspect matching

An approach to the recovery of 3-D volumetric primitives from a single 2-D image is presented. The approach first takes a set of 3-D volumetric modeling primitives and generates a hierarchical aspect representation based on the projected surfaces of the primitives; conditional probabilities capture the ambiguity of mappings between levels of the hierarchy. From a region segmentation of the input image, the authors present a formulation of the recovery problem based on the grouping of the regions into aspects. No domain-independent heuristics are used; only the probabilities inherent in the aspect hierarchy are exploited. Once the aspects are recovered, the aspect hierarchy is used to infer a set of volumetric primitives and their connectivity. As a front end to an object recognition system, the approach provides the indexing power of complex 3-D object-centered primitives while exploiting the convenience of 2-D viewer-centered aspect matching; aspects are used to represent a finite vocabulary of 3-D parts from which objects can be constructed     

Introducing a new problem: shape-from-silhouette when the relative positions of the viewpoints is unknown

3D shapes can be reconstructed from 2D silhouettes by back-projecting them from the corresponding viewpoints and intersecting the resulting solid cones. However, in many practical cases as observing an aircraft or an asteroid, the positions of the viewpoints with respect to the object are not known. In these cases, the relative position of the solid cones is not known and the intersection cannot be performed. The purpose of this paper is introducing and stating in a theoretical framework the problem of understanding 3D shapes from silhouettes when the relative positions of the viewpoints are unknown. The results presented provide a first insight into the problem. In particular, the case of orthographic viewing directions parallel to the same plane is thoroughly discussed, and sets of inequalities are presented which allow determining objects compatible with the silhouettes.     

Path similarity skeleton graph matching

This paper presents a novel framework to for shape recognition based on object silhouettes. The main idea is to match skeleton graphs by comparing the shortest paths between skeleton endpoints. In contrast to typical tree or graph matching methods, we completely ignore the topological graph structure. Our approach is motivated by the fact that visually similar skeleton graphs may have completely different topological structures. The proposed comparison of shortest paths between endpoints of skeleton graphs yields correct matching results in such cases. The skeletons are pruned by contour partitioning with Discrete Curve Evolution, which implies that the endpoints of skeleton branches correspond to visual parts of the objects. The experimental results demonstrate that our method is able to produce correct results in the presence of articulations, stretching, and occlusion.     

Non-rigid 3D object retrieval using topological information guided by conformal factors

Combining the properties of conformal geometry and graph-based topological information, a non-rigid 3D object retrieval methodology is proposed, which is both robust and efficient in terms of retrieval accuracy and computation speed. While graph-based methods are robust to non-rigid object deformations, they require intensive computation which can be reduced by the use of appropriate representations, addressed through geometry-based methods. In this respect, we present a 3D object retrieval methodology, which combines the above advantages in a unified manner. Furthermore, we propose a string matching strategy for the comparison of graphs which describe 3D objects.