@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, MG, Brazil",
conference-year = "22-25 Aug. 2012",
doi = "10.1109/SIBGRAPI.2012.30",
url = "http://dx.doi.org/10.1109/SIBGRAPI.2012.30",
language = "en",
ibi = "8JMKD3MGPBW34M/3C9T6SH",
url = "http://urlib.net/ibi/8JMKD3MGPBW34M/3C9T6SH",
targetfile = "PID2450295.pdf",
urlaccessdate = "2024, Apr. 29"
}