Chapter 4: Spontaneous Morphing

Heather Oh - Ryan Cho - Jennifer Tam

Dorsal Simultanagnosia

What exactly is a part?

-

Transversal Intersection:-at points where the two objects join

together(intersect)Concave creases- sharp edges in the surface

that point into the objectConvex creases- sharp edges in the surface

that point out of the object

Rule #14. Rule of concave creases: Divide shapes into parts along concave creases.

-Any object may be an example.-Where things seem to join together.-Where surface degree changes.

Schroder Staircase

-Surface Normals: -Positive-Negative-Zero

MOBIUS STRIP

Main Points:-Surface normals and its connection to concave and

convex creases. Where do they point?-Bubble out of water vs. Bubble inside of water-What do we really pay attention to?-Example: the mushrooms

Principal Curvatures: Positive, Negative, or zero.

Figure & Ground

If the normals point outward, then the principal curvature is positive.If the normals point inward, then the principal curvature is negative.

When the crease has been smoothed, the crease turns into a point ofhigh curvature.

Subjective and Selective Attention-Rule #15. Minima Rule: Divide shapes into parts at negative minima, along lines of curvature, of the principle curvatures.

-Examples: •Fusilli Pasta•Keys•The ‘Ripple’

Ripple

SilhouettesRule #16. Minima rule for silhouettes: Divide silhouettes into parts at concave cusps and negative minima of curvature.

•Examples:

Face & Goblet

Similarity

Symmetry vs. Repetition-Point 1: Repetition should be easier to recognize

because it is the exact same thing (object or image), just repeated. (the corresponding parts are always equally spaced apart)

-Point 2: According to the minima rule, symmetry is easier to see because the curves repeat at the same point and the curvatures of the first object match the second figure.

Rabbit-Duck

The minima rule predicts that you should more easily recognizethe objects on the right than on the left because…

Questions we ask ourselves-What do we notice more?-What should we divide?

Example: CookingRule #17: The Salience of a cusp boundary increases with increasing sharpness of the angle at the cusp. Rule #18: The salience of a smooth boundary increases with the magnitude of normalized curvatures at the boundary.

Rule #19. Salient boundaries: Choose figure and ground so that figure has the more salient part boundaries.

Rule 20: Salient PartsChoose figure and ground so that figure has the more salient parts.

The recognizable difference between the figure and ground of objects is crucial for every day survival and decision making. Without understanding simple tasks such as picking up the butcher knife by the handle as opposed to the blade, would result in unpleasant consequences.

BibliographyHoffman, Dr. Donald D. Visual Intelligence: How we create what we see. 1998. W.W. Norton and Company, Inc. United States of America.

Jongen, Hubertus Th., Jonker, Peter, Twilt, Frank. Nonlinear Optimization in Finite Dimensions: Morse Theory, Chebyshev Approximation, Transversality, Flows, Parametric Aspects. 2000. Kluwer Academic Publishers. Netherlands.

Also, we used images downloaded from www.google.com and www.yahoo.com