Parisian camera placement for vision metrology

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Abstract

This paper presents a novel camera network design methodology based on the Parisian evolutionary computation approach. This methodology proposes to partition the original problem into a set of homogeneous elements, whose individual contribution to the problem solution can be evaluated separately. A population comprised of these homogeneous elements is evolved with the goal of creating a single solution by a process of aggregation. The goal of the Parisian evolutionary process is to locally build better individuals that jointly form better global solutions. The implementation of the proposed approach requires addressing aspects such as problem decomposition and representation, local and global fitness integration, as well as diversity preservation mechanisms. The benefit of applying the Parisian approach to our camera placement problem is a substantial reduction in computational effort expended in the evolutionary optimization process. Moreover, experimental results coincide with previous state of the art photogrammetric network design methodologies, while incurring in only a fraction of the computational cost.

Introduction

Planning a photogrammetric network with the aim of obtaining a high-accurate 3D object reconstruction is considered as a challenging design problem in vision metrology (Fraser, 1996). This design problem offers an intricate combination of interactions between the sensor physical constraints, the mathematical modeling of the problem, as well as the numerical methods used to solve it (Wong and Kamel, 2004, Chen and Li, 2004). Building on previous research on automated sensor placement, we develop a novel methodology for sensor placement based on the Parisian approach to evolutionary computation (EC). The Parisian approach of individual evolution considers that a single individual represents a partial solution to the considered problem. Hence, a process of aggregation of multiple individuals is needed in order to arrive at a solution. We incorporate such an approach to the camera network design problem by evolving a population of camera subnetworks. As a result, computational requirements are greatly reduced for individual fitness evaluation due to the reduced size of the total mathematical model. Parisian evolution is a complex optimization technique because multiple new aspects need to be considered in the evolutionary computation framework, such as: problem partitioning and representation, local fitness evaluation, global fitness evaluation and redistribution, population diversity preservation, and finally aggregation of individuals. In this paper, we attempt to combine widely accepted principals and techniques used in EC research. On the other hand, in the case of radical new concepts we provide a first solution based on the characteristics of the studied problem. Previous works have used what is called the Parisian approach. The work of Collet et al. (2000) can be considered the first attempt to use the concept of individual evolution applied to the problem of iterate function systems within the domain of genetic programming. Louchet et al. (2002) use also Parisian evolution for a problem of stereo vision, which could be seen as the first work in the evolution strategies domain.

Vision metrology addresses the attainment of accurate visual measurements from digital images. The choice of an adequate imaging geometry plays a major role in this process (Fraser, 1996). The process by which the best possible configuration can be automatically determined, is still an open research area. Today, practitioners generally rely on heuristic means for making these crucial decisions. On the other hand, the problem of 3D reconstruction from multiple redundant image measurements is very well studied in photogrammetry and can be rigorously solved using iterative non-linear optimization techniques (McGlone, 2004). Nevertheless, the lack of a widespread utilization of network design inside the photogrammetric community can be attributed to the inherent design complexity and its expensive computational requirements. Photogrammetric network design requires complex spatial reasoning about the geometrical characteristics of an object and the mathematical modeling of optical triangulation. This reasoning is by no means trivial and has been the topic of very diverse research.

For example, the work of Mason (1997) solves the problem of camera placement by incorporating considerable a priori knowledge into an expert system. In this way, a set of heuristics based on the theory of generic networks is used to model the decision making process. On the other hand, the work of Olague and Mohr (2002) uses an evolutionary computation approach, developing a criterion based on the error propagation phenomena, which was further extended considering a bundle adjustment (Olague, 2002). In this way, the required spatial reasoning is carried out by and adaptive system based on stochastic meta-heuristics that yield human competitive results. Recently, the work of Saadatseresht et al. (2004) addresses the problem of improving an existing camera network by positioning additional sensing stations based on what they term “visibility uncertainty prediction modeling”. This new modeling is based on the concepts of visibility uncertainty prediction and visibility uncertainty spheres. These concepts provide a mechanism to predict the visibility of current object target points in order to improve the overall certainty. All the above works give special attention to the usefulness of rigorous approaches such as bundle adjustment in order to characterize the quality of the photogrammetric network. In particular, the works of Fraser, 1987, Olague and Mohr, 2002 have provided insight into how a mathematical modeling could be derived in order to simplify the network design. The aim of this work is to present a new network design simplification based on the numerical optimization approach. This work shows the ongoing development of the EPOCA sensor planning system and implements an evolutionary computation methodology based on the Parisian approach (Dunn et al., 2005). This is accomplished in order to efficiently search the space of possible camera configurations while maintaining high-qualitative solutions of the photogrammetric adjustment process.

This paper is organized as follows. First we briefly introduce the quality criterion we have used to characterize a network configuration. Then, the paradigm of Parisian evolution is presented. A solution to the photogrammetric network design in terms of Parisian evolution is described together with implementation details about the problem partitioning, solution aggregation, individual fitness evaluation and diversity preservation techniques. Finally, experimental results are presented followed by discussion and conclusions.

Section snippets

Criterion for accurate reconstruction

Accuracy assessment of visual 3D reconstruction consists on attaining some characterization of the uncertainty of our results. The design of a photogrammetric network is the process of determining an imaging geometry that allows accurate 3D reconstruction. In order to estimate the 3D reconstruction error as a function of the disposition of multiple cameras, we will use an approach based on the error propagation phenomena as presented in (Olague and Mohr, 2002). Under the pinhole camera model,

The Parisian approach: Evolutionary divide and conquer

The Parisian approach, originally proposed in (Collet et al., 1999), differs from typical approaches to evolutionary computation in the sense that a single individual in the population represents only a part of the problem solution. In this respect, it is similar to the Michigan approach developed for Classifier Systems (Holland, 1975), where a solution is a rule base obtained from an evolved population of individual rule subsets. Moreover, in this paradigm an aggregation of multiple

Parisian approach to camera network design

Camera placement can be viewed as a geometric design problem where the control variables are the spatial positioning and orientation parameters of a finite set of cameras. In order to state such design problem in optimization terms the criterion expressed in Section 2 is adopted. However, due to the sensor characteristics and mathematical modeling of the problem a strongly constrained optimization problem emerges. In this section we will discuss the different implementation issues involved in

Experimental results

The reconstruction of a complex 3D object is considered in our experimentation. The goal is to determine a viewing configuration that will offer optimal results in terms of reconstruction accuracy. Here, we shall consider the design of a fixed size camera network of M = 9 stations. According to our approach, the level of granularity of our problem decomposition needs to be established. For these series of experiments we will use camera subnetworks of N = 3 cameras. In this way, each of the

Conclusions and discussion

The Parisian approach to evolutionary computation offers an efficient way to address the problem of automated camera placement, while preserving the validity of photogrammetric procedures. In fact, by virtue of an adequate problem partition and decomposition, solution quality is improved with considerable reductions in computational effort for the considered scenarios. Future work includes incorporating rigorous bundle adjustment procedures, where the computational savings should be even more

Acknowledgement

This research was funded by CONACyT and INRIA through the LAFMI project 634-212. First author supported by scholarship 142987 from CONACyT.

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