By Y. Aloimonos, C. Fermüller (auth.), Gerald Sommer, Yehoshua Y. Zeevi (eds.)
This quantity provides the complaints of the 2d overseas Workshop on - gebraic Frames for the notion and motion Cycle. AFPAC 2000. held in Kiel, Germany, 10–11 September 2000. The offered themes conceal new leads to the conceptualization, layout, and implementation of visible sensor-based robotics and independent structures. designated emphasis is put on the function of algebraic modelling within the correct disciplines, akin to robotics, laptop imaginative and prescient, idea of multidimensional signs, and neural computation. The goals of the workshop are twofold: ?rst, dialogue of the effect of algebraic embedding of the duty handy at the emergence of latest features of modelling and moment, dealing with the robust kin 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 study paintings during this ?eld, and the diversity of suitable themes was once for this reason broadened, The technique followed by means of this workshop doesn't unavoidably ?t the mainstream of globally research-granting coverage. despite the fact that, its look for primary difficulties in our ?eld may actually bring about new leads to the proper disciplines and give a contribution to their integration in reports of the perception–action cycle.
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Additional info for Algebraic Frames for the Perception-Action Cycle: Second International Workshop, AFPAC 2000, Kiel, Germany, September 10-11, 2000. Proceedings
13) This is a ‘star’, a union of linear functions through the origin, see Fig. 7b. 6 Reconstruction after Sampling In linear ﬁltering, the spatial sampling of a function f is done through multiplication by the impulse train (which is a sum of delta functions). In the frequency domain, this leads to a convolution of the Fourier transform of this train and the spectrum F [f ], leading to a sequence of additively overlapping copies of the original spectrum F [f ] (see Fig. 8b). If those do not overlap, which happens if the original spectrum was band-limited and the sampling was suﬃciently ﬁnegrained (at least twice the highest frequency, this is the Nyquist criterion) one can reconstruct the original signal by multiplication of its spectrum by the bandpass ﬁlter, see Fig.
W. : The morphological structure of images: the diﬀerential equations of morphological scale space. IEEE Trans. on Pattern Analysis and Machine Intelligence 16 (1994) 1101–1113 38 2. : Objects in contact: boundary collisions as geometric wave propagation. In: Geometric Algebra: A Geometric Approach to Computer Vision, Quantum and Neural Computing, Robotics and Engineering, E. Bayro-Corrochano, G. Sobczyk, eds. Birkh¨ auser (2000) Chapter 17, 355–375 26 3. : Morphological signal processing and the slope transform.
This is done as follows. e. as a set of (translation) vectors in the vector space V m in G. Sommer and Y. Y. ): AFPAC 2000, LNCS 1888, pp. 22–47, 2000. c Springer-Verlag Berlin Heidelberg 2000 The Systems Theory of Contact 23 Fig. 1. Two objects in contact in 2-dimensional space. The rightmost example shows how penetration is ‘beyond the double kiss’, changing one of the kisses into penetration; but it makes the curve of kissing positions diﬀerentiable (dashed) which the objects reside. These sets need not be connected: A could represent all the obstacles in a scene, B could be the moving robot.
Algebraic Frames for the Perception-Action Cycle: Second International Workshop, AFPAC 2000, Kiel, Germany, September 10-11, 2000. Proceedings by Y. Aloimonos, C. Fermüller (auth.), Gerald Sommer, Yehoshua Y. Zeevi (eds.)