Estimating Intrinsic Camera Parameters from the Fundamental Matrix Using an Evolutionary Approach
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Estimating Intrinsic Camera Parameters from the Fundamental Matrix Using an Evolutionary Approach Anthony Whitehead School of Computer Science, Carleton University, Ottawa, ON, Canada K1S 5B6 Email: [email protected]
Gerhard Roth National Research Council of Canada, Ottawa, ON, Canada K1A 0R6 Email: [email protected] Received 30 June 2002; Revised 21 October 2003; Recommended for Publication by Stefano Cagnoni Calibration is the process of computing the intrinsic (internal) camera parameters from a series of images. Normally calibration is done by placing predefined targets in the scene or by having special camera motions, such as rotations. If these two restrictions do not hold, then this calibration process is called autocalibration because it is done automatically, without user intervention. Using autocalibration, it is possible to create 3D reconstructions from a sequence of uncalibrated images without having to rely on a formal camera calibration process. The fundamental matrix describes the epipolar geometry between a pair of images, and it can be calculated directly from 2D image correspondences. We show that autocalibration from a set of fundamental matrices can simply be transformed into a global minimization problem utilizing a cost function. We use a stochastic optimization approach taken from the field of evolutionary computing to solve this problem. A number of experiments are performed on published and standardized data sets that show the effectiveness of the approach. The basic assumption of this method is that the internal (intrinsic) camera parameters remain constant throughout the image sequence, that is, the images are taken from the same camera without varying such quantities as the focal length. We show that for the autocalibration of the focal length and aspect ratio, the evolutionary method achieves results comparable to published methods but is simpler to implement and is efficient enough to handle larger image sequences. Keywords and phrases: autocalibration, dynamic hill climbing, fundamental matrix, evolutionary computing, epipolar geometry, 3D reconstruction.
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INTRODUCTION
Calibration is the process of computing internal physical quantities of a camera’s geometry. Parameters such as focal length, center of projection, and CCD sensor array dimensions are required in order to get 3D information from a series of images. Autocalibration has become popular recently because of the desire to create 3D reconstructions from a sequence of uncalibrated images without having to rely on a formal calibration process. The standard calibration model for a pinhole camera has five unknown intrinsic parameters defined in a 3 × 3 calibration matrix (K). These parameters are the focal length, aspect ratio, sensor skew, and the center of projection x and y (the principal point). The accurate estimation of these 5 parameters directly from an image sequence without having a formal calibration process is the goal of autocalibration.
Autocalibration works by computing aforementioned quantities directly
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