Measurements and Scale
On the Gaussian Scale-Space,
Taizo IIJIMA,
IEICE Transactions D: On Information and Systems,
Vol.E86-D No.7 pp.1162-1164 2003/7
Arjan Kuijper,
Dissertation: The deep structure of Gaussian scale space images,
Chapters:
Title,
1,
2 (Gaussian Scale Space),
3,
4,
5,
6,
7,
8
Joachim Weickert, Seiji Ishikawa, Atsushi Imiya,
Scale-Space has been discovered in Japan,
Journal of Mathematical Imaging and Vision,
Technical Report 18, Department of Computer Science, University of Copenhagen, 1997. 162
Derivatives
M. Nielsen et al.,
"Regularization, Scale-Space, and Edge Detection Filters",
Journal of Mathematical Imaging and Vision, vol. 7, no. 4, pp. 291-307, 1997.
J. Blom, B. ter Haar Romeny, A. Bel, J. J. Koenderink,
"Spatial Derivatives and the Propagation of Noise in Gaussian Scale Space"
Journal of Visual Communication and Image Representation, vol. 4, no. 1, pp 1-13, 1993.
Differential Geometry
Lewis Griffin et al.,
Superficial and deep structure in linear diffusion scale space:
Isophotes, critical points and separatrices
Feature detection and scale selection:
T. Lindeberg,
"Feature detection with automatic scale selection",
International Journal of Computer Vision, vol. 30, no. 2, pp. 79-116, 1998.
T. Lindberg,
"Scale-space: A framework for handling image structures at multiple scales",
technical report, 1996.
T. Lindeberg,
"Edge detection and ridge detection with automatic scale selection",
International Journal of Computer Vision, vol. 30, no. 2, pp. 117-154, 1998.
K. S. Pedersen, M. Nielsen,
"The Hausdorff Dimension and Scale-Space Normalisation of Natural Images",
Journal of Visual Communication and Image Representation, vol. 11, no. 2, pp. 266-277, 2000.
Invariance
Luc Florack et al.
Scale and the differential structure of images
Image and Vision Computing, Vol.10 no.6. july/august 1992 pp.376-388
Luc Florack et al.
Cartisian differential invariances in Scale-space
Journal of mathematical imaging and vision, Vol 3. pp.327-348, 1993
Luc Florack et al.
General intensity transformations and differential invariants
Journal of mathematical imaging and vision, Vol 4, 171-187, 1994
Reconstruction
Feature-based Image Analysis
Optical flow
L. Florack, W. Niessen, M. Nielsen,
"The Intrinsic Structure of Optic Flow Incorporating Measurement Duality",
International journal of computer vision, vol. 27, no. 3, pp. 263-286, 1998.
W. Niessen, J. S. Duncan, M. Nielsen, L. Florack, B. ter Haar Romeny, M. Viergever,
"A Multiscale Approach to Image Sequence Analysis" ,
Computer Vision and Image Understanding, vol. 65, no. 2, pp. 259-268, 1997.
K. Pedersen, M. Nielsen,
"Computing Optic Flow by Scale-Space Integration of Normal Flow", Proceedings of Scale-Space 2001, LNCS 2106, Springer Verlag, July 2001.
Deep Structure
The deep structure of Gaussian scale space images Ch 4-8.
Kuijper, A. Florack, L.M.J.
The hierarchical structure of images
IEEE Transactions on Image Processing, IEEE Transactions on Sept. 2003 Volume: 12, Issue: 9 page(s): 1067- 1079
Singularity Theory
Primary source:
Generic Image Structure, Ole Fogh Olsen, Chapter 3 and Chapter 7
Local Morse theory for Gaussian blurred functions, J.Damon
In Gaussian Scale-Space, Kluwer 1996, ed. Sporring et al
"Multiscale Hierarchical analysis"
"Multiscale Hierarchical Segmentation"
B.Platel, L.M.J. Florack, F.M.W. Kanters, B.M. ter Haar Romeny,
Accepted for Advanced School for Computing and Imaging, ASCI 2003 Conference, June 4-6, 2003.
Watersheds
Ole Fogh Olsen,
Generic Image Structure,
Chapter 4, chapter 9, 10 and 11
Nonlinear Extensions
Pietro Perona and Jitendra Malik,
Scale-Space and Edge Detection Using Anisotropic Diffusion,
IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 12, No 7, July 1990
Supplemental literature:
B.M. ter Haar Romenij,
Front-End Vision and Multi-Scale Image Analysis
Bart M. ter Haar Romeny,
Geometry-Driven Diffusion in Computer Vision
Jon Sporring, Mads Nielsen, Luc Florack, Peter Johansen,
Gaussian Scale-Space Theory
Luc Florack,
Image Structure
J. Weickert,
Anisotropic diffusion in image processing
J. Damon,
Local Morse theory for solutions to the heat equation and Gaussian blurring,
Journal of differential equations, Vol 115, no 2 January 1995
