Download Algebraic Frames for the Perception-Action Cycle: Second by Y. Aloimonos, C. Fermüller (auth.), Gerald Sommer, Yehoshua PDF

By Y. Aloimonos, C. Fermüller (auth.), Gerald Sommer, Yehoshua Y. Zeevi (eds.)

This quantity provides the lawsuits of the 2d foreign Workshop on - gebraic Frames for the conception and motion Cycle. AFPAC 2000. held in Kiel, Germany, 10–11 September 2000. The provided themes conceal new ends up in the conceptualization, layout, and implementation of visible sensor-based robotics and self reliant structures. detailed emphasis is put on the function of algebraic modelling within the correct disciplines, reminiscent of robotics, machine imaginative and prescient, idea of multidimensional indications, and neural computation. The goals of the workshop are twofold: ?rst, dialogue of the impression of algebraic embedding of the duty handy at the emergence of latest characteristics of modelling and moment, dealing with the powerful family among dominant geometric difficulties and algebraic modelling. The ?rst workshop during this sequence, AFPAC’97. encouraged a number of teams to i- tiate new learn courses, or to accentuate ongoing examine paintings during this ?eld, and the variety of suitable themes was once as a result broadened, The process followed by means of this workshop doesn't inevitably ?t the mainstream of globally research-granting coverage. notwithstanding, its look for primary difficulties in our ?eld may actually result in new leads to the appropriate disciplines and give a contribution to their integration in reports of the perception–action cycle.

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Extra resources for Algebraic Frames for the Perception-Action Cycle: Second International Workshop, AFPAC 2000, Kiel, Germany, September 10-11, 2000. Proceedings

Sample text

There are in biological vision several examples available for such properties; edge and line detectors, orientation detectors, etc [3,8]. If we view the channel output as derived from a band pass filter, we can establish a measure of distance or similarity in terms of the parameters of this filter. See Figure 1. For a conventional, linear simple band pass filter, the phase distance between the flanks is a constant π/2. Different filters will have different band widths, but we can view this as a standard unit of similarity or distance, with respect to a particular channel filter.

XK ]T (2) We assume for conceptual simplicity that the numbers k are consecutive integers, directly corresponding to the numbers of consecutive channels. This allows a more consistent treatment and a better understanding of mechanisms. We are obviously free to scale and translate the actual input variable in any desired way, as we map it onto the set of channels. An actual scalar variable ξ can be scaled and translated in the desired way x = scale · (ξ − translation) (3) to fit the interval spanned by the entire set of channels {xk }.

This gives ft (x) ≡ f (x − t) F [·] F −1 F [ft ](ω) = F [f ](ω) × e−iωt [·] In contact systems, translation over t is represented as tangential dilation by the shifted delta-function δt (x) ≡ δ(x − t), of which the Legendre transform is −ωt: L[δt ](ω) = statu [δ(u − t) − ω u] = statv [δ(v) − ω v] − ωt = −ωt This gives ft (x) ≡ f (x − t) L[·] L−1 [·] L[ft ](ω) = L[f ](ω) − ωt Note that the computations in both frameworks run completely analogously. The Systems Theory of Contact 37 Fig. 6. 4 Bandwidth Limitation In linear systems theory, band limitation is achieved through multiplying the spectrum by the ideal bandpass filter H(ω) = 1 if |ω| ≤ ω0 0 if |ω| > ω0 This inverse Fourier transform yields the famous ‘sinc’-function: F −1 [H](x) = ω0 x ω0 sinc( )≡ π π sin ω0 x πx 1 if x = 0 if x = 0 Convolution with this function indeed leads to a limitation of the spectrum of a signal to the frequencies between −ω0 and ω0 , limiting the bandwidth, see Fig.

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