expert system-based design of close-range photogrammetric networks

Designing an appropriate multi-station, convergent n e realization of -accuracy photogrammetric measurement in industrial applications. S approach in which the expertise of the photogrammetrist is relied u overcome the complexity of the task. This article reports on investigations into the feasibility of an expert system solution to the automation of this design task. ajor findings include recommendations for the esentation of networ ology and spatial reformation, the appropriate architecture for an ert system-based tool, dels for camera placement and network diagnosis, and a computational model for camera pl system CGNSENS was built to test these concepts and models. Experiments with it confirm the feasibility of the approach. Prospects for application of this approach in photogrammetric practice, as well as limitations, are identified.

Photogrammetry is well-suite range measurement applications it utilizes non-contact sensors, pe recording, is low-cost relative to ment techniques, is flexible, and measurement accuracies. High measurement accuracies are achieved through the selection of the bundle method as suitable mathematical model of the process, by calibration of the measurement system, and through the careful design of an appropriate convergent, multi-station sensor configuration. Such networks, as illustrated in Fig. 1, are defined by the measurement of an object where all (or at least, most) of the features to be measured appear and are measurable in three or more spa- tially separated images (Granshaw, 1980). Major characteristics of multi-station configurations in- fluencing the achievable triangulation accuracy are as follows.

(1) Observational redundancy. Each object feature is intersected by more than the minimum number of rays (i.e. two) necessary to position it in 3D. This redundancy leads to an improvement in measurement precision, in addition to providing for statistical reliability in the measurement operation.

1 Institute of Geodesy and Photogrammetry, Swiss Federal Institute of Technology, SO93 Zurich, Switzerland.

and pose of the ca

intersections. As a

ture, the better will be the triangulation and with it t easurement precision of the featur

hilst the suitability of close-range metry to diverse applications ranging trial inspection to architecture and bi well demonstrated, this technique has rare applied by other than experienced photogrammetrists. A major contributing factor 1s the expertise needed in the design of the appropriate convergent multi-station network. A software ap-

Figure 1. A convergent multi-station network.

ISPRS Journal of Photogrammetry and Remote Sensing, 50(5): 13-24 0924-2716/95/$09.50 0 1995 Elsevier Science B.V. All rights reserved.

14 ISPRS Journal of Photogrammetry and Remote Sensing

proach to network design employing this expertise is of interest and could potentially bring the following benefits (Mason et al., 1991; Mason, 1994): (I) enable non-experts to make use of photogrammetric methods; (2) provide support for experts in routine network design; and (3) cater for applications areas demanding automatic decision-making (e.g. in flexible manufacturing).

This article presents an overview of the status of photogrammetric network design with particular emphasis on investigations into the feasibility of an exprt system (ES) solution to photogrammetric network design conducted recently at the Institute of Geodesy and Photogrammetry, Swiss Federal Institute of Technology, Zurich. Building an er;pcrt system “is a complex, ill-structured, and inherently experimental activity, i.e. there is little

everything can be figured out beforehand” an et al. (1983). The feasibility of an ES

to a task can therefore only be tested by prototyping (Walters and Nielsen, 1988). This prototyping process generally entails five steps: problem identification, conceptualization, formalization, implementation and testing (Buchanan et al., 1983). The identi’cation step entails selecting the task the ES should solve and defining the re- lated problem domain. In conceptualization, the key attributes of the task and domain are made explicit and structured into a conceptual model. For- malization of knowledge constitutes a mapping of the key concepts, sub-problems and information- flow characteristics isolated during the conceptu- alisation stage into formal, knowledge-engineering representations, such as production rules. Imple- mentation involves mapping the formalized knowledge into the representations supported by the selected ES development shell. In the testing step, the performance of the ES is evaluated, e.g. against some case studies for which solutions exist. Itera- tive revision of the ES, e.g. in the form of redesign of the knowledge representations or reformulation of the task conceptualization, is commonly needed.

This discussion on the use of ESs for network design is structured according to the above- mentioned model of the ES construction process. In Sect. 2 the network design problem domain is described, including a discussion on the corn-- plexity of the camera station placement problem and the current status of network design. Sect. 2.3 reports on a conceptual model for the camera station placement task. In Sect. 3 knowledge rep-

resentational issues ar ssed ing a computational model for reas in camera station placement. Sect. 4 describes development of the prototype ES-based network design system CONSENS. CONSENS (“CONfiguration of SENors Stations”) consists of a commercial system shell, supporting both rule and frame- knowledge representations and hybrid reasoning, a commercial computer-aided design (CAD) package, and in-house developed bundle adjustment software. The prototype was developed for application with a measurement robot, a “closed-world” domain in which automated network design is required. An example network described in Sect. 6 illustrates CONSENS’s practical capabilities. This article concludes with an examination of the potential of ES-based network design and suggestions for future work. As it is not within the scope of this article to report more than major results, the reader is frequently referred to articles containing more detailed information.

esigning close-range ric

2.1. Current status

General network design is the process by which the goal of precise, reliable and economic object measurement is achieved through configuration of a suitable optical triangulation network. It entails finding solutions to four fundamental problems (Grafarend, 1974): zero-order design (ZOD) - defining the measurement datum; first order design (FOD) - configuring the triangulation geometry; second-order design (SOD) - weighting the observations; and third-order design (TOD) - network densification, whereby TOD is irrelevant to the vast majority of close-range photogrammetric applications (Shortis and Hall, 1989). Gra- farend’s model has been adopted by numerous practitioners who, in turn, have classified their network design considerations according to these four problems (e.g. see Fraser, 1984; Shortis and Hall, 1989; Mason, 1994).

The most complex of the design problems in photogrammetric network design is arguably FOD. This task involves such basic decision-making as choosing the number of camera stations and their respective poses. The complexity lies in: (i) the fact that practically an infinite number of possible

Volwae 50, number 5, 1995

of the views; second, so be redundant insofar as

perhaps most importantly, the inspection requirements impose conditions on ho.7 the views are chosen, e.g. for reason accurac at arbitrary views will not satisfy ( shall an artin, 1992; Mason, 1994). Tarbox and Gottschlich proven that a restricted form of F selecting the minimal number of stat cretized search space for complete coverage of a target field with an active triangulation sensor of

elongs to the class of NP-complete 2 ecauss the multi-station configuration

design task involves a greater number of degrees of fresdom and camera placement constraints than Gonsidered by Tarbox and Gottschlich, it can be concluded that a trial-and-error strategy approach to finding an optimal network is not tractable. Thus, heuristic methods which capture the expertise of photogrammetrists are necessary.

The heuristic method employed by photogrammetric experts in network design is termed design- by-simulation. This method orders the three photogrammetric network design problems (ZOD, FOD, SOD) according to the sequence which expert practitioners have found reliably leads to an efficient and effective solution (Fraser, 1984; Schlogelhofer, 1989). Because many of the considerations and constraints in the design problems are interrelated and/or compete, a direct solution is generally not possible and an iterative approach is

1 The economy goal is less relevant to apphcatilons using digi- tal sensors than those using analogue sensors. * A problem is NP (non-deterministic polynomial) complete if its algorithmic complexity is larger than polynomial, e.g. exponential.

22. Software solutions to close-range network design

ile significant advances in improving the speed, interaction metric data reduc automatic feature measurement matching), little progress towards “intelligent” network design has been made. Current network design tools (both commercial and research) do not possess network design expertise. Many can be considered rudimentary, offering little more than the ability to perform bundle adjustment on a simulated network. Commercial tools permit, for example, users to model the objects to be measured in CAD-like environments and to visualize the precision results (e.g. Brown, 1982; Deacon, 1985; Hinsken et al., 1992); however, effective use of these tools still demands expertise on behalf of the user: the network design decisions are made by the user.

Recent years have seen some activity in the direction of software-based photogrammetric network design 3. Zinndorf (1986) and Fritsch and Crosilla (1990) have investigated the potential of analytical FOD in photogrammetric network design. Both approaches optimize given configurations by iteratively shifting the camera stations until the covariance matrix of the estimated target coordinates is better than a criterion matrix. Behr et al. (1988) describe an ES to assist in

--_-- the design of networks employing stereo-ilIld$ng

geometries, e.g. for architectural applications. Pre- liminary studies into the feasibility of expert SYS- tems for network design have been carried out by Bammeke and Baldwin (1992). A knowledge base for camera selection was developed. While these tools and approaches contribute to software-based network design, none offers a practical solution to the FOD task.

The placement of camera stations is clearly also a topic of interest to the machine vision community 4. As reviewed in Mason (1994, 1995b), progress towards the automation of the placement of a single camera station has been made for the task of viewing, but not triangulating, a set of object features from a single viewpoint. One excep- tion is the IVIS system developed by (Tarbox and Gottschlich, 1993), containing a strategy for auto- matically placing multiple stations for 3D object measurement with an active triangulation sensor. Cowan et al. (1990) have also experimented with strategies for placing multiple stations to overcome object occlusions. A practical solution, however, has not yet been reached.

The research reported here represents a first practical solution to the software-based design of multi-station convergent configurations. It sets as goal the exploitation of the knowledge held by network design experts. The appropriate technology for this was deemed to be expert systems (Mason et al., 1991; Mason and Kepuska, 1992a). Following a brief review of this technology, an appropriate domain for ES-based network design is defined.

2.3. Expert systems

Artificial intelligence (AI) emerged during the 1950s and 1960s with one of its goals being to make machines more intelligent and therefore more useful. The development of expert systems as a research area can be linked to a conceptual breakthrough in AI that occurred in the late 1970s involving a shift in tmphasis from formal reasoning

3 Note that advances towards software-based geodetic network design have limited relevance to photogrammetric network design: unlike in the photogrammetric FOD case, there is generally little freedom in selecting geodetic triangulation stations; and the optimizing of the weights of individual observations is more practical in the geodetic case than in photogrammetric network design. 4 The FOD problem is often referred to in the machine vision community as the “sensor placement task”.

methods to an emphasis on knowledge itself: “to make a program intelligent., high-quality, specific knowle lem area” (Waterman, 1986). Thereafter, special- purpose computer programs (systems that contained ‘knowledge in some narrow main) began to be developed. Although a strict definition for these “programs” does not exist, it is generally accepted that an “ES is a computer program intended to emulate the problem-solving behaviour of a human who is expert in a narrow problem domain” (Denning, 1986). Like many AI terms, however, expert system is loaded with a great deal more implied intelligence than is warranted by their actual level of sophistication. Critics of ESs point out that they are not creative, do not learn from experience, need to be told everything, are unable to reason abstractly, have a narrow focus and possess only technical knowledge (Dreyfus and Dreyfus, 1986; Waterman, 1986). Seen from a software engineering standpoint, however, ESs have been successfully applied to a large number of tasks ranging from medical diagnosis, to geological prospecting, to computer hardware configuration and finance.

Careful choice of the domain in which to ap- ply an ES is important. Experiences gained in early ES projects have established a number of criteria defining suitable domains: (i) an algorithmic solution should not exist; (ii) the task should be narrow and knowledge-intensive; (iii) cognitive skills only should be required; (iv) the task must be well understood; (v) genuine experts must exist; and (vi) the task should not be too difficult, or (vii) involve common-sense reasoning (Walters and Nielsen, 1988). ESs are best applied to problems that have limited and well-defined expertise. Evaluating the network design task with respect to the above criteria yields the following (Mason and Kepuska, 1992a; Bammeke and Baldwin, 1992).

(1) Given that FOD is an NP-complete problem heuristic solutions are needed.

(2) Associated with each class of photogrammetric applications is a body of domain-specific knowledge and constraints which often dictate the network design. In order that the domain is sutli- ciently narrow, the ES must be focused on one of these applications.

(3) In open-world environments, such as inspection on the factory floor, the environmental factors are numerous and cannot be predicted.

Figure 2. Concept of a measurement robot.

Network design in such an environment would involve common-sense reasoning. In a cb0sf~&worid environment, such as a robotic work cell, the number of possible events is small and can often be controlled and/or modelled. be constructed with sufficient

eal with each event, common-sense reasoning can be avoided, and the network design task may be automated.

(4) The large number of successful photogrammetric applications provides sufficient proof of the existence of network design experts.

(5) Network design requires only cognitive and not, e.g., physical skills.

Since the network design domain fulfils many of the ES prerequisites, aprima facie case in favour of the feasibility of an expert system approach is established. In these investigations, automation of network design in the context of a measurement robot was set as goal.

2.4. Measurement robot

A measurement robat (MR) is defined here to be a flexible inspection cell. Fig. 2 illustrates a conceivable architecture for a measurement robot, consisting of an optical sensor mounted on a robot arm and object-positioned on a controllable turntable. Inspection with such a system involves the following sequence of steps: (1) input a CAD model providing an (approximate) geometrical de-

ace5; (2) trans- s into a set of object points, edges); (3) accurately triangu-

late these features; (4) acquisition of the (5) reduce the data, exploiting the netwo

tion in processing the imagery; desired inspection quantities 6.

was developed to perform st Under the assumption th

with a passive sensor (e.g. classes of inspection tasks of applicability: (i) the precise 3 measurement of key point features; and (ii) when the distribution of point features is sufficiently dense, object surface shape can be controlled. Artificially tar- geting the point features is mandatory when high possible measurem.ent accuracy should be achieved (Granshaw, 1980), although the use of natural or projected point features is accommodated.

5 In the absence of a CAD model the task becomes one of reverse engineering and is not considered here. 6 Functions that the measurement robot will, in addition, need to perform in carrying out these steps include recognizing the object (perhaps), determining the object’s pose with respect tot he robot’s coordinate systems, positioning the sensor to ac- quire the images, feature extraction in the images, and setting up appropriate object illumination. For the sake of simplicity these funetians are not included in Fig. 2 and while they are practical issues, they are less relevant to the discussion in network design here.

ISPRS Journal of Photogrammetry and Remote Sensing

(a) targets are grouped (b) a generic network (c) modification of (d) multiple networks are connected. is selected for each generic network suit target group. e.g. the workspace

Figure 3. Conceptual model for first-order design (FOD) based on generic networks.

3. Conceptual model for camera station ES for network design, it was therefore necessary placement to develop such models.

In the conceptualization stage of building an ES, the knowledge in the specified problem domain is transcribed into a form which serves to ex- pose the strategies, relations and information flow in the domain (Buchanan et al., 1983). This process is an important step in knowledge acquisition (KA). Knowledge is most commonly acquired manually by interviewing experts although this is not without shortcomings. For example, the expert may provide incorrect information, the information may also be misunderstood, or the questions may be bi- ased (see Dreyfus and Dreyfus, 1986; Walters and Nielsen, 1988). For these investigations, initially, a questionnaire covering various aspects of network design was prepared (Mason, 1994). The responses of some twelve network design experts both pro- vided design heuristics later used in CONSENS and confirmed the conceptual model of FOD described below. Some questions posed in the questionnaire, however, proved to be ambiguous and were interpreted differently by the experts. A sub- sequent round of interviews conducted with some of the experts enabled some of the misunderstand- ings to be clarified and contributed to the acquired knowledge.

As pointed out in Mason (1995a), the photogrammetric literature is absent of any knowledge in the form of recipes (methods or models) which indicate how the many design considerations can he applied in network design, e.g. how to decide how many camera stations are needed and where they should be positioned in space? Neither Gra- farend’s scheme nor the simulation strategy (Sect, 2.1) make this knowledge explicit. In building an

The model developed for FO is based on the concept of generic networks. A generic network is defined as a configuration of camera stations that delivers a strong imaging geometry for a class of network design problems. By the term class of network design problems is understood a range of target field geometries for which the generic network delivers at least a satisfactory imaging geometry. Generic networks constitute compiled expertise insofar as each such network consists of a sufficient number of camera stations configured to provide a strong imaging geometry for each target belonging to a target field. The application of generic networks is explained by Fig. 3. Initially, the object’s (or target fidld’s) shape is simplified and decomposed into surface primitives (e.g. planes, boxes, cylinders, parabolic dishes), thereby enabling the grouping of the measurable features into sets. For each set, a generic network suited to the measurement of each primitive surface is recalled. Because the camera station poses suggested by the generic network may not comply with the workspace, the network must be adapted before it can be added to the design. At this stage, and if the object has been decomposed into more than one surface, the networks are still unconnected. Therefore, a fi- nal step is needed in which camera stations are added to the design with the function of connecting the independent sub-configurations together. This generic network model is fully described in Mason (1995a) See Schliigelhofer (1989) for the evaluation of some generic networks in architectural photogsammetry.

The most common generic network is com- prised of multiple stations symmetrically dis-

diagnosis.

In the formalization stage of expert system velopment, domain knowledge is mapped into formal, knowledge-engineering representations. The term knowledge representation refers to the set of conventions by which knowledge, facts or beliefs can be described, i.e. in terms of co er data structures.

4.1. Representing network topology

Photogrammetric networks, consisting of the basic entity types camera stations, images, object target points and image points, are hierarchical structures. The topology of such structures is dynamic during the network design process as, for example, new camera stations are added to the configuration and object points are observed as image points in the images at these new stations. Mason and Kepuska (1992b) demonstrate that frames are well-suited to the representation of these structures. Frames represent items (e.g. a physical object), an idea or hypothesis. Their contents, called slots, describe the item in some way (e.g. its characteristics, properties and/or behaviour). The frame representation naturally fa- cilitates categorizing and structuring diverse data- types in a knowledge base, a framework whereby not only the data, but also the structure of the data can be reasoned with, e.g. in rules, and supports reasoning with dynamic structures (Wal- ters and Nielsen, 1988). Examples of the use of frames in network design can be found in Mason (1994).

esis possible poor reliabi-

ade members of the class

derived from a bundle adjustment. In this manner, the variable and dynamic nature of the network’s topology can be successfully handled.

Rules are a declarative form of representation. In order to solve tasks it is necessary to decide on a strategy for applying the rules. Design problems are often solved in a goal-directed manner and thus best-suited to a backward-chaining reasoning strategy. Diagnostic problems, on the other hand, are usually data- driven with the goals (the faults) being inferred from the observational data. This type of problem- solving is well-suited to forward-chaining reasoning in a rule-based ES. Because network design involves both design and diagnostic tasks, both forward- and backward-reasoning strategies are needed (Mason and Kepuska, 1992b).

4.3. Spatial reasoning in camera station placement

While the use of CAD has certain advantages in network design (see Sect. 5.2.1), CAD model representations are not, however, always ideal for

20 ISPRS Journal of Photogrammetry and Remoie Sensing “P

(a) planview (b) perspective view

Figure 4. Camera station placement using the constraint sphere representation

vision tasks and transformation to an intermediate representation is needed (Bhanu and HO, 1987). In Mason (1994, 1995b) the functional requirements of a representation suitable for network design are discussed. An evaluation of the 3D object representations commonly used in computer graphics, CAD, and computer vision determined that the boundary representation (BRep) satis- fies many of these requirements, including object modelling, visualisation, and hidden-surface com- putations. However, an additional representation was deemed necessary for use in reasoning about camera station placement. Since the placement of sensor stations is a viewing direction problem - where should the sensor he pIaced with respect to the object or target field? - the viewing sphere representation was selected for this task. This representation consists of a sphere positioned with its origin at the centre of the object under inspection. Its radius is set to an appropriate sensor-to-object viewing distance. For computational reasons, the sphere is tessellated with each cell in the tessel- lation representing a discrete viewing direction to the object (e.g. Sakane et al., 1987).

A modified version of the viewing sphere, the constraint sphere representation, was developed for camera station placement reasoning. As shown in Fig. 4, the constraint sphere (CS) is defined as a sphere with origin located at the centre of the current point group and z -axis parallel to the surface normal. The unit sphere is longitude-latitude tessellated at a user-defined resolution, offering the advantage that the polar angles correspond to the two components of imaging geometry: the disttibu- tion of camera stations is a function of longitude, while latitude directly corresponds to the in&a-

tion crf a camera station with respect to the point group. Search for suitable sensor station locations can consequently be simplified into two independent search problems. An optimal distribution of stations is enabled in the selection of distributed search sectors (Fig. 4a). The convergence of the rays is optimized in the manner in which the cells within each sector are searched (Fig. 4b). Here, each cell is tested for a viewing distance d which will satisfy all camera placement constraints. More details on the use of the CS can be found in (Mason, 1995b).

design tool ert system-base

As noted in Sect. 1, the feasibility of an ES solution to a task can only be tested by prototyping. CONSENS was built as a prototype for automating network design in the context of a measurement robot. As illustrated in Fig. 5, CONSENS is com- prised of an ES based on the Nexpert Object shell (hereafter referred to as Nexpert), which supports both rule and frame-based knowledge representations and hybrid reasoning, the computer-aided design (CAD) package AutoCAD, and in-house- developed bundle adjustment software SGAI? 7 CONSENS requires input in the form of precision and reliability specifications, a CAD model, and an observation scheme definition. The CAD model consists of a polyhedral surface description of the object to be measured and the workspace, as described in Sect. 52.1 below. The observation scheme consists of the precision of image measurement and a camera, the latter being defined by its format and pixel dimensions and focal

.

Volume 50, bobber 5, 1995

Figure 5. Architecture and dataflow of CONSENS.

length. These parameters can be altere user. Remaining camera parameters (aperture and constant focus distance) can be determined once all stations have been placed. The role of each of these components is described below.

5.1. Expert system

The ES component in CONSENS possesses knowledge about the design of multi-station convergent configurations by simulation. In this respect, it mimics the decision-making role per- formed by the network design expert. The ES component consists of an ES shell and five domain- specific knowledge bases. A shell in this context is an expert system development tool that provides formal knowledge-engineering ways for representing the knowledge in a problem domain and a standard user interface. Nexpert fulfils the repre- sentational requirements (see Sect. 4) of network design, including rule and frame representations and forward- and backward-chaining.

5.2. Network simulation software

The optimal mathematical model for simulat- ing network designs is the self-calibrating bundle method (Granshaw, 1980; Brown, 1980; Fraser, 1984; Mason and Griin, 1993, in particular, because it supports rigorous (total) error propaga- tion. This is essential if basic indeterminacy or

7 Nexpert Object i s a product of Neuron Data, Inc., Palo Alto, CA. AutoCAD is a product of AutoDESK Inc., Sausalito, CA. SGAP is a modified and extended version of GAP (Beyer, 1992).

external control is

of external constraints.

5.2.1. Computer-aided design (CAD) In order to be able to reason about cam-

era station placement, a network design tool requires spatial information. Computer-aided design (CAD) advantages offer distinct advantages in this respect for both geodetic (see e.g. Cross, 1981) and togrammetric networks (see e.g. Gustafson and own, 1985; Deacon, 1985; Shortis and 1989; Mason and Kepuska, 1992a).

(1) CAD provide a means of geometrically modelling the object in its workspace. Using “sketch” tools, this could be accomplished in a rapid manner thus making the use of CAD also suitable for on-site applications.

(2) CAD improves the realism of the network simulations through hidden-surface removal under perspective views for testing target visibility, the computation of ray incidence angles, and testing the validity of camera stations, e.g. when the object is located within a restrictive workspace. Note, however, that the CAD model of an object under inspection is only approximate and thus these tests are at best also approximate.

(3) CAD models act as a link between the various stages of manufacturing, e.g. product design

22 ISPRS Journal of Photogrammetty and Remote Sensing

and inspection. The choice of CAD model representation is particularly important: it should provide a means to specify tolerance information to both manufacturing and inspection processes (Park and Mitchell, 1988). Current CAD modelling systems do not explicitly contain the geometrical and topological properties useful for vision-based inspection. To compensate for this gap, the CAD representation can be extended to include features which can be detected in images of the object, e.g. corners (Park and Mitchell, 1988).

(4) CAD can play an important role in network visualisation and diagnosis, e.g. by permitting 3D perspective views of the object and workspace and of design quality through, for example, the display of error ellipsoids.

AutoCAD was chosen not only because it ful- filled the above criteria, but also because of its open architecture and applicability to other Insti- tute projects (e.g. Streilein, 1994).

6. Example network design

The following example serves to demonstrate CONSENS’s network design capabilities. Key features positioned on two faces of 160 mm cube- shaped, metallic object were to be inspected to an accuracy of 3~0 01 mm, amounting to a relative

accuracy of 1: 24,000 (see Fig. 6a). The camera designated was the Kodak a CCD sensor 1524 x 10 dimension 9 m*) and a nominal 28 mm lens. Initially, CONSENS decomposed the target fiel into two planar (primitive) surfaces, for each of which a 4-station network was designed (see Figs. 6b and 6~). Then, in order to connect the two independent networks, CONSENS added two additional sensor stations, each measuring targets from both object surfaces (see Fig. 6d). Fig. 6e shows the complete lo-station configuration. The bundle adjustment for the simu!ated design predicted an average point coordination precision of SfO 007 mm, or 1: 35,700. In order to test the validity of this network, and thereby to prove that CONSENS is capable of dealing with real inspection tasks, images were acquired with the DCS200 at each of the sensor stations suggested by CON- SENS’s design. The point features were measured using least-squares template-matching to a precision of 0.05 pixels. A bundle adjustment of this measured data delivered an average point coordination precision of &O 0073 mm, or 1: 34,200. As Fig. 6f illustrates, the error ellipsoids are relatively homogeneous and isotropic. The average reliability number of the observations was 0.68. These precision and reliability results compare well with

(d) connection stations

c;, /\ \

/ 0

0 /’

‘1 0 (b) network for surface 1 (c) network for surface 2

(e) complete IQ-station network (f) scaled error ellipsoids

Figure 6. Example network design by CONSENS.

Since the design of converge networks is an

of CONSENS

here include recommendati

network diagnosis, and a computational model for camera placement.

Prototypes like CONSENS are by definition limited in scope. It is therefore important to ex- amine the scalability and practical potential of this approach. First, it should be noted that C assumes the: (i) availability of a compl model of the working environment and the object to be measured; and (ii) definition of the (limited) set of possible measurement tasks. Such assump- tions are reasonable in the “closed-world” context of a measurement robot. In this role, however, CONSENS is currently limited by the following.

(1) CAD modezling entities. Polyhedral surface descriptions only are supported.

(2) On-line design modification. In the presence of (i) gross inaccuracies in modelling the object and work environment, (ii) incomplete knowledge of the measurement environment, and/or (iii) un- certainty in the object’s pose, the designed network may not satisfy the measurement specifications. Methods for on-line design modification need to be developed which react to improved knowledge about the object geometry and its environment.

(3) Multiple generic networks. CONSENS is currently restricted to the use of a single generic network. An extension to other generic networks is desirable to widen its scope.

(4) Illumination planning. Adequate object illumination is currently assumed through employ-

used in teaching. (2) Extension to other inspection techniques.

The application of this approach to, for example, camera station place ent for active sensors and the measurement of natural features, e.g. edges, should be investigated.

Additional suggestions for further research are reported in (Mason, 1994).

Veton Kepuska contributed to the development of CONSENS with many useful ideas, criticisms and suggestions. The suggestions of an anonymous reviewer helped improve the quality of this paper. Financial support by the Swiss National Research Program 23 (Artificial Intelligence and Robotics) is gratefully acknowledged.

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(Received December 12, 1994; revised and accept,:d February 27, 1995)

expert system-based design of close-range photogrammetric networks

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