TY - GEN

T1 - Adaptive structure tensors and their applications

AU - Brox, Thomas

AU - Van Den Boomgaard, Rein

AU - Lauze, François

AU - Van De Weijer, Joost

AU - Weickert, Joachim

AU - Mrázek, Pavel

AU - Kornprobst, Pierre

N1 - Publisher Copyright: © Springer-Verlag Berlin Heidelberg 2006.

PY - 2006

Y1 - 2006

N2 - The structure tensor, also known as second moment matrix or Förstner interest operator, is a very popular tool in image processing. Its purpose is the estimation of orientation and the local analysis of structure in general. It is based on the integration of data from a local neighborhood. Normally, this neighborhood is defined by a Gaussian window function and the structure tensor is computed by the weighted sum within this window. Some recently proposed methods, however, adapt the computation of the structure tensor to the image data. There are several ways how to do that. This chapter wants to give an overview of the different approaches, whereas the focus lies on the methods based on robust statistics and nonlinear diffusion. Furthermore, the data-adaptive structure tensors are evaluated in some applications. Here the main focus lies on optic flow estimation, but also texture analysis and corner detection are considered.

AB - The structure tensor, also known as second moment matrix or Förstner interest operator, is a very popular tool in image processing. Its purpose is the estimation of orientation and the local analysis of structure in general. It is based on the integration of data from a local neighborhood. Normally, this neighborhood is defined by a Gaussian window function and the structure tensor is computed by the weighted sum within this window. Some recently proposed methods, however, adapt the computation of the structure tensor to the image data. There are several ways how to do that. This chapter wants to give an overview of the different approaches, whereas the focus lies on the methods based on robust statistics and nonlinear diffusion. Furthermore, the data-adaptive structure tensors are evaluated in some applications. Here the main focus lies on optic flow estimation, but also texture analysis and corner detection are considered.

UR - http://www.scopus.com/inward/record.url?scp=84925633450&partnerID=8YFLogxK

U2 - 10.1007/3-540-31272-2_2

DO - 10.1007/3-540-31272-2_2

M3 - Conference article

AN - SCOPUS:84925633450

SP - 17

EP - 47

JO - Mathematics and Visualization

JF - Mathematics and Visualization

SN - 1612-3786

IS - 200709

T2 - Workshop on Visualization and Processing of Tensor Fields, 2004

Y2 - 18 April 2004 through 23 April 2004

ER -