In practice the relevant details of images exist only over a restricted range of scale. Hence it is important to study the dependence of image structure on the level of resolution. It seems clear enough that visual perception treats images on several levels of resolution simultaneously and that this fact must be important for the study of perception. However, no applicable mathematically formulated theory to deal with such problems appears to exist. In this paper it is shown that any image can be embedded in a one-parameter family of derived images (with resolution as the parameter) in essentially only one unique way if the constraint that no spurious detail should be generated when the resolution is diminished, is applied. The structure of this family is governed by the well known diffusion equation (a parabolic, linear, partial differential equation of the second order). As such the structure fits into existing theories that treat the front end of the visual system as a continuous stack of homogeneous layers, characterized by iterated local processing schemes. When resolution is decreased the images becomes less articulated because the extrem ("light and dark blobs") disappear one after the other. This erosion of structure is a simple process that is similar in every case. As a result any image can be described as a juxtaposed and nested set of light and dark blobs, wherein each blob has a limited range of resolution in which it manifests itself. The structure of the family of derived images permits a derivation of the sampling density required to sample the image at multiple scales of resolution.(ABSTRACT TRUNCATED AT 250 WORDS)

In this work, we investigate the visual appearance of real-world surfaces and the dependence of appearance on scale, viewing direction and illumination direction. At ne scale, surface variations cause local intensity variation or image texture. The appearance of this texture depends on both illumination and viewing direction and can be characterized by the BTF (bidirectional texture function). At su ciently coarse scale, local image texture is not resolvable and local image intensity is uniform. The dependence of this image intensity on illumination and viewing direction is described by the BRDF (bidirectional re ectance distribution function). We s i m ultaneously measure the BTF and BRDF of over 60 di erent rough surfaces, each observed with over 200 di erent c o m binations of viewing and illumination direction. The resulting BTF database is comprised of over 12,000 image textures. To enable convenient use of the BRDF measurements, we t the measurements to two recent models and obtain a BRDF parameter database. These parameters can beused directly in image analysis and synthesis of a wide variety of surfaces. The BTF, BRDF, and BRDF parameter databases have important implications for computer vision and computer graphics and and each i s made publicly available.

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A mobile observer samples sequences of narrow-field projections of configurations in ambient space. The so-called structure-from-motion problem is to infer the structure of these spatial configurations from the sequence of projections. For rigid transformations, a unique metrical reconstruction is known to be possible from three orthographic views of four points. However, human observers seem able to obtain much shape information from a mere pair of views, as is evident in the case of binocular stereo. Moreover, human observers seem to find little use for the information provided by additional views, even though some improvement certainly occurs. The rigidity requirement in its strict form is also relaxed. We indicate how solutions of the structure-from-motion problem can be stratified in such a way that one explicitly knows at which stages various a priori assumptions enter and specific geometrical expertise is required. An affine stage is identified at which only smooth deformation is assumed (thus no rigidity constraint is involved) and no metrical concepts are required. This stage allows one to find the spatial configuration (modulo an affinity) from two views. The addition of metrical methods allows one to find shape from two views, modulo a relief transformation (depth scaling and shear). The addition of a third view then merely serves to settle the calibration. Results of a numerical experiment are discussed.

This paper offers a quick review of the subject of "optic flow" in its conceptual and computational aspects. The theory is evaluated in terms of possible applications in the neurophysiology and experimental psychology of spatial sensorymotor behaviour and perception. The problem of which kind of detector is suited to extract various aspects of optic flow is given special attention. It is shown that the possibilities are actually much more various than is reflected in the current (even the frankly speculative) literature. It is argued that a system that is sensitive to the relative time changes of the orientation differences of image details is especially suited for an analysis of the optic flow with regard to the information concerning the three dimensional shape of objects such as is contained in the flow. Thus the orientation sensitive elements that are known to be abundantly present in the primary visual cortex of many vertebrates are hereby implicated as a quite likely substrate for the extraction of the solid shape of environmental objects. In our opinion this possibility should be investigated with the same ardour as the usual interpretation, which holds this system responsible for the initial extraction of the contours of flat (i.e. defined in the image) shapes. A new, partial solution to the "structure from motion problem" is offered, that not only covers the usual case of shape extraction in the presence of rigid motions of the object, but also the much wider class of (non-rigid) bending deformations (such as occur in the non-rigid deformations of inextensible shells). These solutions violate all conditions required by the well known "structure from motion theorem": the solutions are possible for point configurations in which no fourtuple of points moves as a rigid structure and for input data from merely two views. A numerical example illustrates how this algorithm can be used to predict side views of an object from very limited input data.

It is shown that a convolution with certain reasonable receptive field (RF) profiles yields the exact partial derivatives of the retinal illuminance blurred to a specified degree. Arbitrary concatenations of such RF profiles yield again similar ones of higher order and for a greater degree of blurring. By replacing the illuminance with its third order jet extension we obtain position dependent geometries. It is shown how such a representation can function as the substrate for "point processors" computing geometrical features such as edge curvature. We obtain a clear dichotomy between local and multilocal visual routines. The terms of the truncated Taylor series representing the jets are partial derivatives whose corresponding RF profiles closely mimic the well known units in the primary visual cortex. Hence this description provides a novel means to understand and classify these units. Taking the receptive field outputs as the basic input data one may devise visual routines that compute geometric features on the basis of standard differential geometry exploiting the equivalence with the local jets (partial derivatives with respect to the space coordinates).

We employ an optimal solution to both the "shape from motion problem" and the related problem of the estimation of self-movement on a purely optical basis to deduce practical rules of thumb for the limits of the optic flow information content in the presence of perturbation of the motion parallax field. The results are illustrated and verified by means of a computer simulation. The results allow estimates of the accuracy of depth and egomotion estimates as a function of the accuracy of data sampling and the width of field of view, as well as estimates of the interaction between rotational and translational components of the movement.

Abstract. A new theorem is discussed that relates the apparent curvature of the occluding contour of a visual shape to the intrinsic curvature of the surface and the radial curvature. This theorem allows the formulation of general laws for the apparent curvature, independent of viewing distance and regardless of the fact that the rim (the boundary between the visible and invisible parts of the object) is a general, thus twisted, space curve. Consequently convexities, concavities, or inflextions of contours in the retinal image allow the observer to draw inferences about local surface geometry with certainty. These results appear to be counterintuitive, witness to the treatment of the problem by recent authors. It is demonstrated how well-known examples, used to show how concavities and convexities of the contour have no obvious relation to solid shape, are actually good illustrations of the fact that convexities are due to local ovoid shapes, concavities to local saddle shapes.