Differential invariants are contrasted with geometric invariants.
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In 1926 he wrote a dissertation " Differential Invariants of Inversive Geometry " for his doctoral degree.
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Invariants constructed using covariant derivatives up to order n are called n-th order " differential invariants ".
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He also made contributions to the theory of differential equations, in particular the development of the theory of differential invariants or criticoids.
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This relation is provided by taking the above differential invariant spacetime interval, then dividing by ( " cdt " ) 2 to obtain:
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A differential invariant is a function on " Y " ( " k " ) that is invariant under the prolongation of the group action.
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The topic of projective geometry is itself now divided into many research subtopics, two examples of which are projective algebraic geometry ( the study of differential invariants of the projective transformations ).
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When Gaussian derivative operators and differential invariants are used in this way as basic feature detectors at multiple scales, the uncommitted first stages of visual processing are often referred to as a " visual front-end ".
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The differential edge detector described below can be seen as a reformulation of Canny's method from the viewpoint of differential invariants computed from a scale space representation leading to a number of advantages in terms of both theoretical analysis and sub-pixel implementation.
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More generally, differential invariants can be considered for mappings from any smooth manifold " X " into another smooth manifold " Y " for a Lie group acting on the Cartesian product " X " & times; " Y ".
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