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Local Solid Shape

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ABSTRACT

Local solid shape applies to the surface curvature of small surface patches—essentially regions of approximately constant curvatures—of volumetric objects that are smooth volumetric regions in Euclidean 3-space. This should be distinguished from local shape in pictorial space. The difference is categorical. Although local solid shape has naturally been explored in haptics, results in vision are not forthcoming. We describe a simple experiment in which observers judge shape quality and magnitude of cinematographic presentations. Without prior training, observers readily use continuous shape index and Casorati curvature scales with reasonable resolution.

No MeSH data available.


The parabolic curves drawn on a copy bust of the Apollo Belvedere (property of the Mathematics Institute of Göttingen).
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fig8-2041669515604063: The parabolic curves drawn on a copy bust of the Apollo Belvedere (property of the Mathematics Institute of Göttingen).

Mentions: Alberti conceived of the local shapes as qualities that were spread over surfaces like paint. That is one reason why we developed the shape index color scale (Koenderink & van Doorn, 1992). One easily imagines a solid body to be painted in these shape index colors. Of course, it remains a matter of experimental phenomenology to explore to what extent observers can actually “see” such distributions. So far, we have collected only scattered observations. Yet, this topic has very attractive potential applications. Well-known is Felix Klein’s speculation that the beauty of human faces is to be sought in the shape of the loci of cups and caps, the yellow and blue isochromes, technically the parabolic curves. Felix Klein had a patient student trace these curves on a copy bust of the Apollo Belvedere (of arcane classical beauty!), an item that still survives at the Mathematics Institute of Göttingen (Figure 8). It is not known how the student managed to do this, nor is there any indication that Klein’s hypothesis was supposed to be verified or contradicted (Hilbert & Cohn-Vossen, 1932). Now, more than a century later (!) we are still in no position to assess the value of this surprising brain wave.Figure 8.


Local Solid Shape
The parabolic curves drawn on a copy bust of the Apollo Belvedere (property of the Mathematics Institute of Göttingen).
© Copyright Policy - creative-commons
Related In: Results  -  Collection

License 1 - License 2 - License 3
Show All Figures
getmorefigures.php?uid=PMC5016822&req=5

fig8-2041669515604063: The parabolic curves drawn on a copy bust of the Apollo Belvedere (property of the Mathematics Institute of Göttingen).
Mentions: Alberti conceived of the local shapes as qualities that were spread over surfaces like paint. That is one reason why we developed the shape index color scale (Koenderink & van Doorn, 1992). One easily imagines a solid body to be painted in these shape index colors. Of course, it remains a matter of experimental phenomenology to explore to what extent observers can actually “see” such distributions. So far, we have collected only scattered observations. Yet, this topic has very attractive potential applications. Well-known is Felix Klein’s speculation that the beauty of human faces is to be sought in the shape of the loci of cups and caps, the yellow and blue isochromes, technically the parabolic curves. Felix Klein had a patient student trace these curves on a copy bust of the Apollo Belvedere (of arcane classical beauty!), an item that still survives at the Mathematics Institute of Göttingen (Figure 8). It is not known how the student managed to do this, nor is there any indication that Klein’s hypothesis was supposed to be verified or contradicted (Hilbert & Cohn-Vossen, 1932). Now, more than a century later (!) we are still in no position to assess the value of this surprising brain wave.Figure 8.

View Article: PubMed Central - PubMed

ABSTRACT

Local solid shape applies to the surface curvature of small surface patches—essentially regions of approximately constant curvatures—of volumetric objects that are smooth volumetric regions in Euclidean 3-space. This should be distinguished from local shape in pictorial space. The difference is categorical. Although local solid shape has naturally been explored in haptics, results in vision are not forthcoming. We describe a simple experiment in which observers judge shape quality and magnitude of cinematographic presentations. Without prior training, observers readily use continuous shape index and Casorati curvature scales with reasonable resolution.

No MeSH data available.