TY - GEN

T1 - A comparison of the deep structure of alpha-scale spaces

AU - Duits, R.

AU - Kanters, F.M.W.

AU - Florack, L.M.J.

AU - Haar Romenij, ter, B.M.

PY - 2005

Y1 - 2005

N2 - We compare the topology and deep structure of alternative scale space representations, so called α-scale spaces, 1/2 ≤ α ≤ 1, which are subject to a first order pseudo partial differential equation on the upper half plane {(x,s) ∈ ℝ d ×ℝ|s > 0}. In particular, the cases α = 1 and α = 1/2, which correspond to respectively Poisson scale space and Gaussian scale space, are considered. Poisson scale space is equivalent to harmonic extension to the upper half plane, inducing potential physics, whereas Gaussian scale space is generated by the diffusion equation on the upper half plane, inducing heat physics. Despite the continuous connection (by parameter 1/2 ≤ α ≤ 1) between these scale spaces and the similarity between their convolution convolution kernels, we show both theoretically and experimentally that there is a strong difference between the topology in the deep structure of these scale spaces.

AB - We compare the topology and deep structure of alternative scale space representations, so called α-scale spaces, 1/2 ≤ α ≤ 1, which are subject to a first order pseudo partial differential equation on the upper half plane {(x,s) ∈ ℝ d ×ℝ|s > 0}. In particular, the cases α = 1 and α = 1/2, which correspond to respectively Poisson scale space and Gaussian scale space, are considered. Poisson scale space is equivalent to harmonic extension to the upper half plane, inducing potential physics, whereas Gaussian scale space is generated by the diffusion equation on the upper half plane, inducing heat physics. Despite the continuous connection (by parameter 1/2 ≤ α ≤ 1) between these scale spaces and the similarity between their convolution convolution kernels, we show both theoretically and experimentally that there is a strong difference between the topology in the deep structure of these scale spaces.

U2 - 10.1007/11577812_21

DO - 10.1007/11577812_21

M3 - Conference contribution

SN - 3-540-29836-3

SN - 978-3-540-29836-6

T3 - Lecture Notes in Computer Science (LNCS)

SP - 234

EP - 248

BT - Deep Structure, Singularities, and Computer Vision

A2 - Olsen, O.F.

A2 - Florack, L.M.J.

A2 - Kuijper, A.

PB - Springer

CY - Berlin

ER -