Gaussian scale space from insufficient image information

TY - GEN

T1 - Gaussian scale space from insufficient image information

AU - Loog, Marco

AU - Lillholm, Martin

AU - Nielsen, Mads

AU - Viergever, Max A.

N1 - Conference code: 4

PY - 2003

Y1 - 2003

N2 - Gaussian scale space is properly defined and well-developed for images completely knownand defined on the d dimensional Euclidean space Rd. However, as soon as image information is only partly available, say, on a subset V of Rd, the Gaussian scale space paradigm is not readily applicable and one has to resort to different approaches to come to a scale space on V. Examples are the theory dealing with scale space on Zd ¿ Rd, i.e., discrete scale space; the approach based on the heat equation satisfying certain boundary conditions; and the ad hoc approaches dealing with (hyper)rectangular images, e.g. zero-padding of the area outside of V, or periodic continuation of the image. We propose to solve the foregoing problem for general V from a Bayesian viewpoint. Assuming that the observed image is obtained by linearly sampling a real underlying image that is actually defined on the complete d dimensional Euclidean space, we can infer this latter image and from that image build the scale space. Re-sampling this scale space then gives rise to the scale space on V. Necessary for inferring the underlying image is knowledge on the linear apertures (or receptive field) used for sampling this image, and information on the prior over the class of all images.

AB - Gaussian scale space is properly defined and well-developed for images completely knownand defined on the d dimensional Euclidean space Rd. However, as soon as image information is only partly available, say, on a subset V of Rd, the Gaussian scale space paradigm is not readily applicable and one has to resort to different approaches to come to a scale space on V. Examples are the theory dealing with scale space on Zd ¿ Rd, i.e., discrete scale space; the approach based on the heat equation satisfying certain boundary conditions; and the ad hoc approaches dealing with (hyper)rectangular images, e.g. zero-padding of the area outside of V, or periodic continuation of the image. We propose to solve the foregoing problem for general V from a Bayesian viewpoint. Assuming that the observed image is obtained by linearly sampling a real underlying image that is actually defined on the complete d dimensional Euclidean space, we can infer this latter image and from that image build the scale space. Re-sampling this scale space then gives rise to the scale space on V. Necessary for inferring the underlying image is knowledge on the linear apertures (or receptive field) used for sampling this image, and information on the prior over the class of all images.

U2 - 10.1007/3-540-44935-3_53

DO - 10.1007/3-540-44935-3_53

M3 - Article in proceedings

SN - 978-3-540-40368-5

T3 - Lecture notes in computer science

SP - 757

EP - 769

BT - Scale Space Methods in Computer Vision

A2 - Griffin, Lewis D.

A2 - Lillholm, Martin

PB - Springer

T2 - 4th International Conference on Scale Space Methods in Computer Vision

Y2 - 10 June 2003 through 12 June 2003

ER -