Robust Algorithms for Object Localization

  • Authors:

  • Aaron Wallack;Dinesh Manocha

  • Affiliations:

  • Computer Science Division, University of California, Berkeley, CA 94720. E-mail: awallack@cognex.com;Department of Computer Science, University of North Carolina, Chapel Hill, NC 27599-3175. E-mail: manocha@cs.unc.edu

  • Venue:
  • International Journal of Computer Vision
  • Year:
  • 1998

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Abstract

Model-based localization, the task of estimating anobject‘s pose from sensed and corresponding model features, is afundamental task in machine vision. Exact constant timelocalization algorithms have been developed for the case where thesensed features and the model features are the same type. Still, itis not uncommon for the sensed features and the model features tobe of different types, i.e., sensed data points may correspond tomodel faces or edges. Previous localization approaches have handleddifferent model and sensed features of different types via samplingand synthesizing virtual features to reduce the problem of matchingfeatures of dissimilar types to the problem of matching features ofsimilar types. Unfortunately, these approaches may be suboptimalbecause they introduce artificial errors. Other localizationapproaches have reformulated object localization as a nonlinearleast squares problem where the error is between the sensed dataand model features in image coordinates (the Euclidean image errormetric). Unfortunately, all of the previous approaches whichminimized the Euclidean image error metric relied on gradientdescent methods to find the global minima, and gradient descentmethods may suffer from problems of local minima. In this paper, wedescribe an exact, efficient solution to the nonlinear leastsquares minimization problem based upon resultants, linear algebra,and numerical techniques. On a SPARC 20, our localization algorithmruns in a few microseconds for rectilinear polygonal models, a fewmilliseconds for generic polygonal models, and one second forgeneralized polygonal models (models composed of linear edges andcircular arcs).