This paper presents the measurement of object reflectance from color images. We exploit the Gaussian scalespace paradigm to de£ne a framework for the robust measurement of object reflectance from color images. Illumination and geometrical invariant properties are derived from a physical reflectance model based on the Kubelka-Munk theory. Imaging conditions are assumed to be white illumination and matte, dull object or general object, respectively, summarized by: shadow highlights illumination illumination intensity color

Although traditional scale-space theory provides a well-founded framework for dealing with image structures at different scales, it does not directly address the problem of how to select appropriate scales for further analysis. This paper introduces a new tool for dealing with this problem. A heuristic principle is proposed stating that local extrema over scales of different combinations of normalized scale invariant derivatives are likely candidates to correspond to interesting structures. Support is given by theoretical considerations and experiments on real and synthetic data. The resulting methodology lends itself naturally to two-stage algorithms; feature detection at coarse scales followed by feature localization at ner scales. Experiments on blob detection, junction detection and edge detection demonstrate that the proposed method gives intuitively reasonable results.

: The problem of scale in shape from texture is addressed. The need for (at least) two scale parameters is emphasized; a local scale describing the amount of smoothing used for suppressing noise and irrelevant details when computing primitive texture descriptors from image data, and an integration scale describing the size of the region in space over which the statistics of the local descriptors is accumulated. A novel mechanism for automatic scale selection is proposed, based on normalized derivatives. It is used for adaptive determination of the two scale parameters in a multi-scale texture descriptor, the windowed second moment matrix, which is defined in terms of Gaussian smoothing, first order derivatives, and non-linear pointwise combinations of these. The same scale-selection method can be used for multi-scale blob detection without any tuning parameters or thresholding. The resulting texture description can be combined with various assumptions about surface texture in order to ...

The purpose of this report 1 is to define optic flow for scalar and density images without using a priori knowledge other than its defining conservation principle, and to incorporate measurement duality, notably the scale-space paradigm. It is argued that the design of optic flow based applications may benefit from a manifest separation between factual image structure on the one hand, and goal-specific details and hypotheses about image flow formation on the other. The approach is based on a physical symmetry principle known as gauge invariance. Data-independent models can be incorporated by means of admissible gauge conditions, each of which may single out a distinct solution, but all of which must be compatible with the evidence supported by the image data. The theory is illustrated by examples and verified by simulations, and performance is compared to several techniques reported in the literature. 1 Introduction The conventional "spacetime" representation of a movie as...

This paper sketches several aspects of a hypothetical cortical architecture for visual object recognition, based on a recent computational model. The scheme relies on modules for learning from examples, suchas Hyperbf-likenetworks, as its basic components. Such models are not intended to be precise theories of the biological circuitry but rather to capture a class of explanations we call Memory-Based Models (MBM) that contains sparse population coding, memory-based recognition and codebooks of prototypes. Unlike the sigmoidal units of some artificial neural networks, the units of MBMs are consistent with the usual description of cortical neurons as tuned to multidimensional optimal stimuli. We will describe howan example of MBM may be realized in terms of cortical circuitry and biophysical mechanisms, consistent with psychophysical and physiological data. A number of predictions, testable with physiological techniques, are made.

A major problem in computer vision for decades concerned the representation of the differential structure of the jet bundle of an input image in a way robust to noise and consistent with the input data. Consequently the description of local and global image properties remained unfeasible for quite a long time. We show that on the basis of physical assumptions it is necessary to describe the differential structure of an input image in terms of one-parameter families of images that are similarity solutions of the spatially isotropic diffusion equation underlying the observation process. These images represent the differential structure of the input image at a continuous range of resolutions or scales. Knowing these scaled versions of the differential structure we give a coordinate independent multi-scale description of an input image: by means of implicit differentiation, dioeerential geometry and homology we may compute local and global invariants of manifolds implicitly de...

We present a new method of multi-resolution image analysis that gives us the most concise set of local orthogonally invariant features of 2-dimensional input images. Solving the equivalence problem corresponding to a local jet and the group of orthogonal transformations of the cartesian coordinate frame we nd a complete and irreducible set of local algebraic invariants that may describe any local orthogonally invariant feature of the jet.

Abstract. This article shows how a (linear) scale-space representation can be de ned for discrete signals of arbitrary dimension. The treatment is based upon the assumptions that (i) the scale-space representation should be de ned by convolving the original signal with a one-parameter family of symmetric smoothing kernels possessing a semi-group property, and (ii) local extrema must not be enhanced when the scale parameter is increased continuously. It is shown that given these requirements the scale-space representation must satisfy the di erential equation@tL = A ScSpL for some linear and shift invariant operator A ScSp satisfying locality, positivity, zero sum, and symmetry conditions. Examples in one, two, and three dimensions illustrate that this corresponds to natural semi-discretizations of the continuous (second-order) di usion equation using di erent discrete approximations of the Laplacean operator. In a special case the multi-dimensional representation is given by convolution with the onedimensional discrete analogue of the Gaussian kernel along each dimension.

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A scene induces spatio-temporal structure on a physical observable over all levels of resolution. Analysis and description of this structure therefore requires a multi-scale approach: differential geometric and topological properties of the scene obtain only then a functional meaning because of the observation process. In this paper a new method is presented for description of the scaled differential geometric and topological structure of the scene. The method is based on the connection imposed by the observable on the space-time continuum. It results in a complete set of orthogonal invariants for D+1-dimensional observed scenes: the intrinsic dynamics of (multi)local and global differential geometric and topological properties for each scene such as a time-dependent optic flow field may be operationalized. In order to extract the desired features like curvatures and Euler numbers the connection on space-time is induced by degenerated geometric structures in the scene that a...