A Scale Selection Principle for Estimating Image Deformations

Tony Lindeberg

Technical report ISRN KTH NA/P--96/16--SE. Department of Numerical Analysis and Computing Science, Royal Institute of Technology, S-100 44 Stockholm, Sweden, Apr 1996.

Extended version in Image and Vision Computing, vol. 16, no. 14, pp. 961--977, 1998.

Shortened version in: Proc.~5th International Conference on Computer Vision, (Cambridge, MA), June 1995, pages 134-141. IEEE Computer Society Press.


A basic functionality of a vision system concerns the ability to compute deformation fields between different images of the same physical structure. This article advocates the need for incorporating explicit mechanisms for scale selection in this context, in algorithms for computing descriptors such as optic flow and for performing stereo matching. A basic reason why such a mechanism is essential is the fact that in a coarse-to-fine propagation of disparity or flow information, it is not necessarily the case that the most accurate estimates are obtained at the finest scales. The existence of interfering structures at fine scales may make it impossible to accurately match the image data at fine scales. selecting deformation estimates from the scales that minimize the (suitably normalized) uncertainty over scales. A specific implementation of this idea is presented for a region based differential flow estimation scheme. It is shown that the integrated scale selection and flow estimation algorithm has the qualitative properties of leading to the selection of coarser scales for larger size image structures and increasing noise level, whereas it leads to the selection of finer scales in the neighbourhood of flow field discontinuities. The latter property may serve as an indicator when detecting flow field discontinuities and occlusions.

Keywords: affine transformation, scale selection, image correspondence, optic flow, shape estimation, stereo, motion, texture, disparity, vergence, invariance, deformation, decomposition, singular value, second moment matrix, surface model, enforced consistency, visual front-end, scale-space, computer vision

Postscript: (805 kb)

PDF: (726 kb)

Background: (Earlier technical report) (Scale selection for feature detection) (Review paper on principles for automatic scale selection) (Monograph on scale-space theory)

Responsible for this page: Tony Lindeberg