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@InProceedings{Castro:2012:InSiCu,
               author = "Castro, Pedro Machado Manh{\~a}es de",
                title = "Invariance for Single Curved Manifold",
            booktitle = "Proceedings...",
                 year = "2012",
               editor = "Freitas, Carla Maria Dal Sasso and Sarkar, Sudeep and Scopigno, 
                         Roberto and Silva, Luciano",
         organization = "Conference on Graphics, Patterns and Images, 25. (SIBGRAPI)",
            publisher = "IEEE Computer Society",
              address = "Los Alamitos",
             keywords = "invariance, pattern recognition, developable surface.",
             abstract = "Recently, it has been shown that, for Lambert illumination model, 
                         solely scenes composed by developable objects with a very 
                         particular albedo distribution produce an (2D) image with isolines 
                         that are (almost) invariant to light direction change. In this 
                         work, we provide and investigate a more general framework; and we 
                         show that, in general, the requirement for such invariances is 
                         quite strong, and is related to the differential geometry of the 
                         objects. More precisely, it is proved that single curved 
                         manifolds, i.e., manifolds such that at each point there is at 
                         most one principal curvature direction, produce invariant 
                         isosurfaces for a certain relevant family of energy functions. In 
                         the three-dimensional case, the associated energy function 
                         corresponds to the classical Lambert illumination model with 
                         albedo. This result is also extended for finite-dimensional scenes 
                         composed by single curved objects.",
  conference-location = "Ouro Preto",
      conference-year = "Aug. 22-25, 2012",
             language = "en",
           targetfile = "PID2450295.pdf",
        urlaccessdate = "2021, Jan. 27"
}


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