Generic neighborhood operators

Scale-Space Theory in Computer Vision

1997

This article shows how a linear scale-space formulation previously expressed for spatial domains extends to spatio-temporal data. Starting from the main assumptions that: (i) the scale-space should be generated by convolution with a semi-group of filter kernels and that (ii) local extrema must not be enhanced when the scale parameter increases, a complete taxonomy is given of the linear scale-space concepts that satisfy these conditions on spatial, temporal and spatio-temporal domains, including the cases with continuous as well as discrete data.Key aspects captured by this theory include that: (i) time-causal scale-space kernels must not extend into the future, (ii) filter shapes can be tuned from specific context information, permitting mechanisms such local shifting, shape adaptation and velocity adaptation, all expressed in terms of local diffusion operations.Receptive field profiles generated by the proposed theory show high qualitative similarities to receptive field profiles recorded from biological vision.£ Earlier versions of this manuscript have been presented at

Section: Introductionmentioning

confidence: 99%

Linear spatio-temporal scale-space

Scale-Space Theory in Computer Vision

1997

“…Philosophically, this need arises from the fact that we perceive real-world structures as meaningful entities only over certain ranges of scale. Traditionally, m ulti-scale concepts such a s p yramids (Burt 1981Crowley 1981 and scale-space representation (Witkin 1983Koenderink 1984Yuille and Poggio 1986Koenderink and van Doorn 1992Florack 1993Lindeberg 1994 The support from the Swedish Research Council for Engineering Sciences, TFR, and the Esprit-NSF collaborationDi usion is gratefullyacknowledged.Address: KTH, NADA, S-100 44 Stockholm, Sweden. Email: tony@bion.kth.se, danielf@bion.kth.se.…”

Section: Introductionmentioning

confidence: 99%

Scale-space with casual time direction

Lecture Notes in Computer Science

Fagerström

1996

101

This article presents a theory for multi-scale representation of temporal data. Assuming that a real-time vision system should represent the incoming data at di erent time scales, an additional causality constraint arises compared to traditional scale-space theory|we can only use what has occurred in the past for computing representations at coarser time scales. Based on a previously developed scale-space theory in terms of noncreation of local maxima with increasing scale, a complete classi cation is given of the scale-space kernels that satisfy this property of non-creation of structure and respect the time direction as causal. It is shown that the cases of continuous and discrete time are inherently di erent.For continuous time, there is no non-trivial time-causal semi-group structure. Hence, the time-scale parameter must be discretized, and the only way to construct a linear multi-time-scale representation is by ( c a scade) convolution with truncated exponential functions having (possibly) di erent time constants. For discrete time, there is a canonical semi-group structure allowing for a continuous temporal scale parameter. It gives rise to a Poisson-type temporal scale-space. In addition, geometric moving average kernels and time-delayed generalized binomial kernels satisfy temporal causality and allow for highly e cient implementations.It is shown that temporal derivatives and derivative approximations can be obtained directly as linear combinations of the temporal channels in the multi-time-scale representation. Hence, to maintain a representation of temporal derivatives at multiple time scales, there is no need for other time bu ers than the temporal channels in the multi-time-scale representation.The framework presented constitutes a useful basis for expressing a large class of algorithms for computer vision, image processing and coding.

“…One such approach, based primarily on theoretical considerations, is the scale-space representation, i n troduced by Witkin (1983) and Koenderink (1984). Perhaps the most important conclusion of this theory is that if the low-level operators are unbiased in the sense that they do not single out particular locations, orientations, or sizes, then the only permissible linear operations are convolutions with Gaussian kernels and their derivatives at various scales (Koenderink and van Doorn, 1992Florack et al, 1992Lindeberg, 1994a). …”

mentioning

confidence: 99%

Direct computation of shape cues using scale-adapted spatial derivative operators

Gårding

1996

Int J Comput Vision

116

100

This paper addresses the problem of computing cues to the three-dimensional structure of surfaces in the world directly from the local structure of the brightness pattern of either a single monocular image or a binocular image pair.It is shown that starting from Gaussian derivatives of order up to two at a range of scales in scale-space, local estimates of (i) surface orientation from monocular texture foreshortening, (ii) surface orientation from monocular texture gradients, and (iii) surface orientation from the binocular disparity gradient can be computed without iteration or search, and by using essentially the same basic mechanism.The methodology is based on a multi-scale descriptor of image structure called the windowed second moment matrix, which is computed with adaptive selection of both scale levels and spatial positions. Notably, this descriptor comprises two scale parameters a local scale parameter describing the amount of smoothing used in derivative computations, and an integration scale parameter determining over how large a region in space the statistics of regional descriptors is accumulated.Experimental results for both synthetic and natural images are presented, and the relation with models of biological vision is brie y discussed.