Automated Photogrammetric Network Design Using Genetic Algorithms

This work describes the use of genetic algorithms for automating the photogrammetric network design process. When planning a photogrammetric network, the cameras should be placed in order to satisfjr a set of interrelated and competing constraints. Furthermore, when the object is threedimensional, a combinatorial problem occurs. Genetic algorithms are stochastic optimization techniques, which have proved useful for solving computationally difficult problems with high combinatorial aspects. A system based on genetic algorithms, EPOCA (Evolving Positions of CAmeras), was implemented using a three-dimensional CAD integace. The system provides the attitude of each camera in the network, taking into account the imaging geometry, as well as several major constraints such as visibility, convergence angle, and workspace constraint. EPOCA reproduces configurations reported in the photogrammetric literature. Moreover, the system can design networks for several adjoining planes and complex objects, opening interesting new research avenues. Introduction Photogrammetric network design is the process of placing cameras in order to perform photogrammetric tasks. An important aspect of any close-range photogrammetric system is to achieve an optimal spatial distribution of the cameras comprising the network. Planning an optimal photogrammetric network for some special purpose, such as for monitoring structural deformation or for determining the precise shape characteristics of an object, demands special attention from the quality of the network design. Previous approaches to photogrammetric network design have attempted to identify the main stages in the process. Following the widely accepted classification scheme of Grafarend (1974), network design has been divided into four design stages from which only the first three are used in closerange photogrammetry (Fraser, 1984): Zero-Order Design (ZOD): This stage attempts to define an optimal datum in order to obtain accurate object point coordinates and exterior orientation parameters. First-Order Design (FOD): This stage involves defining an optimal imaging geometry which, in turn, determines the accuracy of the system. Second-Order Design (SOD): This stage is concerned with adopting a suitable measurement precision for the image coordinates. It consists usually in taking multiple images from each camera station. Third-Order Design (TOD): This stage deals with the impmvement of a network through the inclusion of additional points in a weak region. Photogrammetric measurement operations attempt to satisfy, Departamento de Ciencias de la Computacibn, Divisi6n de Fisica Aplicada, Centro de Investigaci6n Cientifica y de Educaci6n Superior de Ensenada, B.C., Km. 107 Carretera TijuanaEnsenada, 22860, Ensenada, B.C., M6xico ([email protected]). in an optimal manner, several objectives such as precision, reliability, and economy. The z o D and SOD are greatly simplified in comparison to the geodetic networks for which the four stages were originally developed. Indeed FOD, the design of network configuration or the sensor placement task, needs to be comprehensively addressed for photogrammetric projects. This design stage must provide an optimal imaging geometry and convergence angle for each set of points placed over a complex object (Fraser, 1996). Photogrammetrists have acknowledged the degree of expertise needed to carry out a photogrammetric project. For example, Mason and Griin (1995) developed a work called CONSENS that follows the expert system approach and uses multiple cameras in combination with optical triangulation. It outlines a method of overcoming the set of constraints and objectives presented in camera station placement. The method is based on the theory of generic networks, which constitutes compiled expertise, describing an ideal configuration .of four camera stations that can be employed to provide a strong imaging geometry for the class of planar network design problems. Complex objects are divided into planes; each plane is evaluated through one of these networks and then connected with some additional cameras with the purpose of establishing just one common datum. However, the expert system approach has shown it unlikely that full automation of the network design process will be achieved, due in large part to the human expert's extensive use of commonsense reasoning (Fraser, 1996). On the other hand, the Grafarend classification just presented serves the photogrammetric user by identifying wh-at set of tasks needs to be implemented in designing a network. Despite the progress that photogrammetrists have made in understanding this design problem, the photogrammetric measurement technique has rarely been applied by other than experienced photogrammetrists. Although its definition seems simple, it reaches a high complexity mainly due to the numerous constraints and design decisions that need to be made. Photogrammetric network design is also difficult to obtain due to the unknown number of configurations all having very similar accuracy, but with a very different imaging geometry. Consequently, photogrammetric network design in many machine vision applications is often conducted in atrialand-error fashion or by using heuristic reasoning strategies (Mason, 1997). These strategies fail at solving the problem for the case of complex objects. Moreover, the main question, how to obtain an initial configuration with an optimal imaging geometry, is unsolved and left as the responsibility of the designer. The motivation of this research is to reduce the cost of vision system design and to equip autonomous inspection sysPllc~tograinlllet~.ic: Engint?ering & Remote Scnsing Vol. 68. No. 5. May 2002, pp. 423-431. 0099-1 112/02/b805-42~3S~3.00/0 ( ( ' 1 2002 American Soc:iety f'or Photograr~lmetry a n d Relnote S ~ ? l ~ s i n g PHOTOGRAMMmUC ENGINEERING & REMOTE SENSING Figure 1. Photogrammetric network simulation of four robots. Each camera is mounted on the robot's hand, with the goal of measuring the box on the table. I"; g ? , tems with photogrammetric network capabilities, e.g., measurement robots used in flexible manufacturing (see Figure 1). Expert photogrammetrists regard simulation as a viable strategy for the problem of photogrammetric network design (Fraser, 1996). Computer simulation of close-range photogrammetric networks has been successfully employed and, with the sophistication of computers, a considerable boost to interactive network design has been achieved. The process of photogrammetric network design optimization through computer simulation can follow a number of approaches. One traditional procedure is based on the ZOD, FOD, and SOD stages. Given the criteria related to required triangulation precision, the initial step is to adopt a suitable observation and measuring scheme (the FOD stage). This entails the selection of an appropriate camera format, focal length, and image measurement system, as well as a first approximation to suitable network geometry. Once this design stage is finished, the network is evaluated against the specified criteria. If the network fails to achieve the criteria, a new stage to diagnose and identify the problem is performed. The FOD or SOD will be applied to produce the new solution. If both corrections are insufficient, a completely new network will be proposed until a solution to the problem is achieved. In this way, network design is iterative in nature. The aim of this paper is to present a new simulation-based method for solving the most fundamental stage in network design, i.e., configuring an optimal imaging geometry. The problem is set in terms of a global optimization design (Olague, 1998), which is capable of managing the problem using an adaptive strategy. It explores the solution space using both non-continuous optimization and combinatorial search. The approach then is to minimize the uncertainty of the three-dimensional measurements using as a criterion the average variance of the 3D object points, presuming that the optimization satisfies a number of primary constraints. Emphasis in this paper is given to the optimization process using a genetic algorithm's strategy and how the primary constraints and design decisions are managed to overcome the computational burden. Figure 2 shows a flow diagram of the algorithm detailed in this paper. This paper is organized as follows: first, the bundle adjustment, the mathematical model universally accepted by photogrammetrists, is reviewed in order to obtain a criterion useful to the optimization process. Later, the camera placement reasoning is introduced. Then, a brief summary of the constraints on network design is presented. The problem of photogrammetric network design in terms of a stochastic global optimizaI