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IEEE Transactions on Pattern Analysis and Machine Intelligence
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COLT '93 Proceedings of the sixth annual conference on Computational learning theory
Bounding the Vapnik-Chervonenkis dimension of concept classes parameterized by real numbers
COLT '93 Proceedings of the sixth annual conference on Computational learning theory
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IEEE Transactions on Pattern Analysis and Machine Intelligence
Applying VC-dimension analysis to object recognition
ECCV '94 Proceedings of the third European conference on Computer vision (vol. 1)
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AAAI'94 Proceedings of the twelfth national conference on Artificial intelligence (vol. 2)
Bounding the Vapnik-Chervonenkis Dimension of Concept Classes Parameterized by Real Numbers
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Information and Computation
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STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
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Journal of Computer and System Sciences - Special issue: 26th annual ACM symposium on the theory of computing & STOC'94, May 23–25, 1994, and second annual Europe an conference on computational learning theory (EuroCOLT'95), March 13–15, 1995
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IEEE Transactions on Pattern Analysis and Machine Intelligence
Introduction to the Special Issue on Interpretation of 3-D Scenes-Part I
IEEE Transactions on Pattern Analysis and Machine Intelligence - Special issue on interpretation of 3-D scenes—part I
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IEEE Transactions on Pattern Analysis and Machine Intelligence
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IEEE Transactions on Pattern Analysis and Machine Intelligence
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ECCV '92 Proceedings of the Second European Conference on Computer Vision
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ECCV '92 Proceedings of the Second European Conference on Computer Vision
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ICPR '96 Proceedings of the 1996 International Conference on Pattern Recognition (ICPR '96) Volume I - Volume 7270
Image Analysis and Mathematical Morphology
Image Analysis and Mathematical Morphology
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We analyze the amount of data needed to carry out various model-based recognition tasks in the context of a probabilistic datacollection model. We focus on objects that may be described as semi-algebraicsubsets of a Euclidean space. This is a very rich class thatincludes polynomially described bodies, as well as polygonalobjects, as special cases. The class of object transformations considered is wide, and includes perspective and affine transformations of 2D objects, and perspective projections of 3D objects.We derive upper bounds on the number of data features (associatedwith non-zero spatial error) which provably suffice for drawingreliable conclusions. Our bounds are based on a quantitative analysisof the complexity of the hypotheses class that one has to choosefrom. Our central tool is the VC-dimension, which is a well-studiedparameter measuring the combinatorial complexity of families of sets.It turns out that these bounds grow linearly with the taskcomplexity, measured via the VC-dimension of the class of objects onedeals with. We show that this VC-dimension is at most logarithmic inthe algebraic complexity of the objects and in the cardinality of themodel library.Our approach borrows from computational learning theory. Both learning and recognition use evidence to infer hypotheses but asfar as we know, their similarity was not exploited previously.We draw close relations between recognition tasks and a certain learnability framework and then apply basic techniques of learnabilitytheory to derive our sample size upper bounds. We believe that other relations between learning procedures and visual tasks exist and hope that this work will trigger further fruitful studyalong these lines.