By Jan J. Koenderink, Andrea van Doorn (auth.), Ole Fogh Olsen, Luc Florack, Arjan Kuijper (eds.)
This publication constitutes the completely refereed post-proceedings of the 1st foreign Workshop on Deep constitution, Singularities, and laptop imaginative and prescient, DSSCV 2005, held in Maastricht, The Netherlands in June 2005.
The 14 revised complete papers and eight revised poster papers offered have been conscientiously reviewed and chosen for inclusion within the e-book. They signify the present state of the art in realizing the relation among structural, topological details represented through singularities and metric info of indications, shapes, photographs, and colours.
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Additional info for Deep Structure, Singularities, and Computer Vision: First International Workshop, DSSCV 2005, Maastricht, The Netherlands, June 9-10, 2005, Revised Selected Papers
The effect of two subsequent A1 A3 transitions removing these two parts would have the same impact on the essential loop (albeit that then no closed loop remains). e. the MA lines connecting the top left tail to the nose of the fish. It is easily found as the subset A3  − A, A − B, B − C, C − F, F − A3 . The MA segments in the complete pre-SS is shown in Figure 6a see  for more details on deriving this structure and its left-right ordering. One can see 4 extra diagonal intersecting part, representing the four other MA branches, labelled 2,3, 5, and 6.
The numerator of α is zero precisely when the contact is A4 ; see below for this case. The denominator being zero is the exceptional case noted above. A4 : We ﬁnd t(s, u) = t20 s2 + t11 su + t02 u2 + . . ; v(s, u) = t02 s2 + t11 su + t20 u2 + . . , (10) Pre-symmetry Sets of 3D Shapes 47 and the constant coeﬃcients tij are determined by the local geometry of the surface, namely t02 = 3(d0 κ21 −2d0 κ1 κ2 +b1 c1 κ1 −b1 c1 κ2 +b21 b2 +d0 κ22 ) (κ1 −κ2 )(c1 κ2 −c1 κ1 −2b1 b2 ) t20 = t02 + b1 /(κ1 − κ2 ), t11 = 43 t02 .
Let e1 , e2 be principal directions at p and f1 , f2 principal directions at q. Finally we use κ1 , κ2 for the principal curvatures of M and λ1 , λ2 for the principal curvatures of N . The Jacobian matrix of G at (0, 0, 0, 0, r0) has the following vectors for its columns, using the fact that diﬀerentiating the normal in a principal direction e produces the corresponding principal curvature times e: (1 − rκ1 )e1 , (1 − rκ2 )e2 , −(1 − rλ1 )f1 , −(1 − rλ2 )f2 , m − n (4) Note that m − n is parallel to the chord joining p and q, by (3).