Aspect Graph Research Articles

What defines a view?

At a given instant we see only visible surfaces, not an object's complete 3D appearance. Thus, objects may be represented as discrete ‘views’ showing only those features visible from a limited range of viewpoints. We address how to define a view using Koenderink's (Koenderink & Van Doorn, Biol. Cybernet. 32 (1979) 211.) geometric method for enumerating complete sets of stable views as aspect graphs. Using objects with known aspect graphs, five experiments examined whether the perception of orientation is sensitive to the qualitative features that define aspect graphs. Highest sensitivity to viewpoint changes was observed at locations where the theory predicts qualitative transitions, although some transitions did not affect performance. Hypotheses about why humans ignore some transitions offer insights into mechanisms for object representation.

Topological recognition of polyhedral objects from multiple views

The aspect graph (AG) has been proposed as a viewer-centered tool for object recognition. Although the aspects could be used for recognition from one image, the full information stored in the AG (aspects and visual events) suggests a multiple views, possibly active, approach. The topological nature of the AG also suggests a topological match of images of the unknown object and stored aspects. In this paper we present a theoretical investigation on the use of the AG for topological recognition from multiple views of polyhedral objects. First, we discuss the topological matching process, and give a suitable topological definition of aspect. Moreover, since topological identification is approximate, we tackle the problem of understanding the ability of the AG to topologically discriminate different objects. More precisely, we address the question: how “similar” are two polyhedra with the same AG? The isomorphism of polyhedra is chosen as the reference similarity condition. The cases of general and convex polyhedra are discussed under perspective and parallel projections. In practice, it could be difficult to identify the visual events from the images of the unknown object. Thus, we also compare isomorphism and the similarity induced by: (i) a topologically reduced aspect graph; (ii) the set of topologically different aspects, neglecting visual events.

Computing unique three-dimensional object aspects representation

Abstract This paper presents a new method for representing two-dimensional (2-D) views of three-dimensional (3-D) objects based on aspect graphs. Each view is represented as a unique tree that is further encoded as a string of numbers, different for each topologically different view. This method enables a consistent and efficient way of indexing the aspects in an image structure graph or an aspect database. The objects considered in the paper are polyhedral solids, but the method can be easily extended to any class of objects. Furthermore, the complexities and experimental results for the sequential and parallel versions are presented.

On Computing Structural Changes in Evolving Surfaces and their Appearance

As a surface undergoes a one-parameter family of deformations, its shape and its appearance change smoothly except at certain critical parameter values where abrupt structural changes occur. This paper considers the case of surfaces defined as the zero set of smooth density functions undergoing a Gaussian diffusion process and addresses the problem of computing the critical parameter values corresponding to structural changes in the parabolic curves of a surface and in its aspect graph. An algorithm based on homotopy continuation and curve tracing is proposed in the case of polynomial density functions, whose zero set is an algebraic surface. It has been implemented and examples are presented.

Temporally coherent conservative visibility

Efficiently identifying polygons that are visible from a changing synthetic viewpoint is an important problem in computer graphics. Even with hardware support, simple algorithms like depth-buffering cannot achieve interactive frame rates when applied to geometric models with many polygons. However, a visibility algorithm that exploits the occlusion properties of the scene to identify a superset of visible polygons, without touching most invisible polygons, could achieve fast frame rates while viewing such models.In this paper, we present a new approach to the visibility problem. The novel aspects of our algorithm are that it is temporally coherent and conservative; for all viewpoints the algorithm overestimates the set of visible polygons. As the synthetic viewpoint moves, the algorithm reuses visibility information computed for previous viewpoints. It does so by computing visual events at which visibility changes occur, and efficiently identifying and discarding these events as the viewpoint changes. In essence, the algorithm implicitly constructs and maintains a linearized portion of an aspect graph, a data structure for representing visual events. We demonstrate that the visibility algorithm significantly accelerates rendering of several test models.

Entity-based aspect graphs: Making viewer centered representations more efficient

The aspect graph, a graphical representation of an object's characteristic views has been widely developed by several researchers. However, researchers have stated that aspect graphs are limited due to their high complexity and computational cost. A simple non-convex object, such as a step, has 71 distinct characteristic views (nodes in the aspect graph); more complicated objects could have thousands of characteristic views (nodes). Many characteristic views of an aspect graph are not necessary for many applications. In this paper, a new entity-based aspect graph, EAG, is proposed based on the observation that, for most applications, the visibility of only some of the entities on the object is important. The objects of interest are polyhedral solids. We present algorithms for constructing new entity-based aspect graphs based on the faces, edges and vertices of the object, and for combining and contracting previously constructed EAGs in a database to generate EAGs for new objects. The computation time for construction is reduced, yet sufficient information is provided to the application.

Hot curves for modelling and recognition of smooth curved 3D objects

Major advances in object representation, modelling and matching are required to develop vision systems capable of recognizing complex curved 3D objects observed in monocular images from a large database of models. In this paper, we propose to represent smooth curved 3D shapes by a set of curves where the surface admits high-order tangents. These HOT curves have two remarkable properties: they determine the structure of the image contours and its catastrophic changes, and there is a natural correspondence between two of them (parabolic and limiting bitangent curves) and monocular image features (contour inflections and bitangents). We present a method for automatically constructing these two curves from continuous sequences of video images and describe an approach to object recognition using viewpoint-dependent monocular image features as indexes into a database of models and as a basis for pose estimation. We have implemented both algorithms and present results obtained from real images. We briefly discuss the construction of the whole set of HOT curves and its application to aspect graph construction from image data.

On Computing Aspect Graphs of Smooth Shapes from Volumetric Data

In this paper we address the problem of computing the aspect graph of an object from volumetric image data, with applications in medical image analysis and interpretation. Anatomical surfaces are assumed to be smooth and are identified as the zero set of a three-dimensional density function (e.g., a CT, MR, or ultrasound image). The orthographic-projection aspect graph is constructed by partitioning the view sphere at infinity into maximal regions bounded by visual event curves. These events are the intersections of the view sphere with surfaces ruled by singular tangent lines that graze the object's surface along a set of critical curves. For each visual event the proposed algorithm constructs a new density function from the original one and its derivatives, and computes the corresponding critical curve as the intersection of the object's surface with the zero set of the new density function. Once the critical curves have been traced, the regions of the sphere delineated by the corresponding visual events are constructed through cell decomposition, and a representative aspect is constructed for each region by computing the occluding contour for a sample viewing direction. An implementation of the proposed approach has been constructed and experiments with synthetic data and real medical data are presented. Extensions to the sectional imaging case are also discussed.

Finite-resolution aspect graphs of polyhedral objects

We address the problem of computing the aspect graph of a polyhedral object observed by an orthographic camera with limited spatial resolution, such that two image points separated by a distance smaller than a preset threshold cannot be resolved. Under this model, views that would differ under normal orthographic projection may become equivalent, while "accidental" views may occur over finite areas of the view space. We present a catalogue of visual events for polyhedral objects and give an algorithm for computing the aspect graph and enumerating all qualitatively different aspects. The algorithm has been fully implemented and results are presented.

Using Aspect Graphs to Control the Recovery and Tracking of Deformable Models

Active or deformable models have emerged as a popular modeling paradigm in computer vision. These models have the flexibility to adapt themselves to the image data, offering the potential for both generic object recognition and non-rigid object tracking. Because these active models are underconstrained, however, deformable shape recovery often requires manual segmentation or good model initialization, while active contour trackers have been able to track only an object's translation in the image. In this paper, we report our current progress in using a part-based aspect graph representation of an object14 to provide the missing constraints on data-driven deformable model recovery and tracking processes.

The enumerative geometry of projective algebraic surfaces and the complexity of aspect graphs

The aspect graph is a popular viewer-centered representation that enumerates all the topologically distinct views of an object. Building the aspect graph requires partitioning viewpoint space in view-equivalent cells by a certain number of visual event surfaces. If the object is piecewise-smooth algebraic, then all visual event surfaces are either made of lines having specified contacts with the object or made of lines supporting the points of contacts of planes having specified contacts with the object. In this paper, we present a general framework for studying the enumerative properties of line and plane systems. The context is that of enumerative geometry and intersection theory. In particular, we give exact results for the degrees of all visual event surfaces coming up in the construction of aspect graphs of piecewise-smooth algebraic bodies. We conclude by giving a bound on the number of topologically distinet views of such objects.

Convex hulls, occluding contours, aspect graphs and the Hough transform

The Hough transform is a standard technique for finding features such as lines in images. Typically, edgels or other features are mapped into a partitioned parameter or Hough space as individual votes. The target image features are detected as peaks in the Hough space. In this paper we consider not just the peaks but the mapping of the entire shape boundary from image space to the Hough parameter space. We analyse this mapping and illustrate correspondences between features in Hough space and image space. Using this knowledge we present an algorithm to construct convex hulls of arbitrary 2D shapes with smooth and polygonal boundaries as well as isolated point sets. We also demonstrate its extension to the 3D case. We then show how this mapping changes as we move the origin in image space. The origin can be considered as a vantage point from which to view the object, and the occluding contour can be extracted easily from Hough space as those points where R = 0. We demonstrate the potential for tracking of transitions in the mapping to be used to construct an aspect graph of arbitrary 2D and 3D shapes.

A Method for Model-Based Object Recognition Using Sequential Images

This paper describes a method of object recognition based on aspect graph using the Dempster-Shafer theory. The method deals with several sequential images as input images, and extracts basic probability of the model objects for each input image. The basic probability represents ambiguous information for object discrimination. Our approach combines basic probability which is extracted from each image based on Dempster-Shafer's rule for combining. We have applied our approach to the discrimination of objects. The experimental results show higher reliability than conventional Baysian approach.

Comments on "Efficiently computing and representing aspect graphs of polyhedral objects"

This correspondence is originated by the definition of aspect given in the above paper by Gigus-Canny-Seidel (ibid., vol.13, no.6 (1991)) on the computation of aspect graphs of polyhedra. Simple examples are presented which show that the data stored according to this definition can be unsuitable for identifying an object or its attitude through a topological match. A definition is suggested which does not incur the problems pointed out.

A view-based neurocomputational system for relational map-making and navigation in visual environments

Abstract Artificial navigation systems stand to benefit greatly from learning maps of visual environments, but traditional map-making techniques are inadequate in several respects. This paper describes an adaptive, view-based, relational map-making system for navigating within a 3D environment defined by a spatially distributed set of visual landmarks. Inspired by an analogy to learning aspect graphs of 3D objects, the system comprises two neurocomputational architectures that emulate cognitive mapping in the rat hippocampus. The first architecture performs unsupervised place learning by combining the “What” with the “Where”, namely through conjunctions of landmark identity, pose, and egocentric gaze direction within a local, restricted sensory view of the environment. The second associatively learns action consequences by incorporating the “When”, namely through conjunctions of learned places and coarsely coded robot motions. Together, these networks form a map reminiscent of a partially observable Markov decision process, and consequently provide an ideal neural substrate for prediction, environment recognition, route planning, and exploration. Preliminary results from real-time implementations on a mobile robot called MAVIN (the Mobile Adaptive VIsual Navigator) demonstrate the potential for these capabilities.

Aspect graphs and their use in object recognition

Previous researchers have described several different approaches to 3-D object recognition based on using an iterative technique to control the matching of features from the 2-D projection of a 3-D model to observed image features. The major problem encountered with such approaches is how to automatically choose starting parameter estimates in a manner which both avoids recognition errors due to local minima and is still reasonably efficient. This paper investigates the use of theaspect graph to address this problem. The basic idea is quite simple — an iterative solution is generated for each of a set of candidate aspects and the best of these is chosen as the recognized view. Two assumptions are required in order for this approach to be valid: (1) the iterative search for the correct candidate aspect must converge to the correct answer, and (2) the solution found for the correct aspect must be better than that found for any of the incorrect candidate aspects. In order to explore the validity of these assumptions, a simple aspect graph-based recognition system was implemented. Experiments were carried out using both real and simulated data. The results indicate that the underlying assumptions are generally valid, and that this approach has advantages over previous techniques which incorporated an iterative search.

An Investigation into the Use of Physical Modeling for the Prediction of Various Feature Types Visible from Different Viewpoints

Given that aspect graph and viewsphere-based object recognition systems provide a valid mechanism for 3D object recognition of man-made objects, this paper provides a flexible, automated, and general purpose technique for generating the view information for each viewpoint. An advantage of the work is that the technique is unaffected by object complexity because each step makes no assumptions about object shape. The only limitation is that the object can be described by a boundary representation. A second advantage is that the technique can include other feature types such as specularity. The reason for this is that raytracing techniques are used to simulate the physical process of image generation. Hence it is extendible to visible features resulting from effects due to lighting, surface texture, color, transparency, etc. The work described in this paper shows how occluding and nonoccluding edge-based features can be extracted using image processing techniques and then parametrized and also how regions of specularity can be predicted and described. The use of physical modeling enables situations to be simulated and predicted that are intractable for CAD-based methods (e.g., multiscale feature prediction). An advantage of the method is that the interface between the technique and the raytracing module is a rendered image. Should better physics-based image formation algorithms become available, then they could replace the raytracing module with little modification to the rest of the method.

Generating a hierarchical aspect graph based on multiple range data

AbstractThis paper proposes a method of producing an aspect graph from multiple range data. Generally, when an object is of complex shape, the search of its shape and posture become more difficult, since the number of aspects necessarily increases. To solve this problem, a hierarchical aspect graph (an expanded idea of the aspect graph) is introduced. After a projection range image has been divided into regions based on its differential geometrical features, the viewpoint space is also divided referring to the difference of topologies on the zero‐crossing surface of a scale space. Hierarchical events by which a viewpoint space is divided are obtained by analyzing changes of the topology of the differential geometrical features caused by a viewpoint and resolution at feature points. A reliable aspect graph is produced by interpolating unobserved events due to the limited data of viewpoints and resolutions. The viewpoint space is divided coarsely in its upper structure, and densely in its lower structure. This makes an efficient search of the shape, position and posture of an object based on the coarse‐to‐fine tactic. Three‐dimensional aspect graphs based on real range‐finder input data were processed. The results show the usefulness of the proposed method for identifying the shapes, positions and postures of objects and analyzing moving images.

Introducing the reduced aspect graph

Aspect graphs (AGs) have been proposed as viewer centered representations of 3D objects, suitable for recognizing objects from single or multiple views. Many algorithms for computing the AGs of various categories of objects have been presented; however, very few AG-based recognition applications have been developed. One reason for the limited practical use of AGs is the impressive growth of the information stored as the complexity of the object increases. This may imply comparing the views of the unknown object with a very high number of stored views, and therefore a time-consuming recognition process. The purpose of this paper is to introduce a new kind of aspect graph representation, the reduced aspect graph (RAG). RAGs are suitable for topological object recognition from single or multiple views, and require less information to be stored. Therefore, the matching process is shortened.

Aspect graphs for visual recognition of three-dimensional objects.

Visual representation of three-dimensional (3-D) objects in our environment is a crucial question, for human as well as for machine vision. Some basics are reviewed of a viewer-centred model of 3-D objects, aspect graphs, which represents a 3-D object by all its topologically stable visible image contours (its aspects) and by the transitions between stable image contours (the visual events). This representation takes only geometrical information about discontinuities in depth and in surface orientation into account, and other clues, such as shadows, markings, texture, etc, are disregarded. Mathematical results give some insight into the relationships between the geometry of a 3-D object and the aspect of its image contours, the techniques used to compute an aspect graph effectively, and the state of the art of this type of model in computer vision. Current research is reviewed on viewer-centred representation in cognitive science that seems to indicate that aspect graphs could also have some relevance for human vision.