Last update: April 15, 2004

BACK

Publications by Harry Blum et al. on shape symmetry elicitation :

• 3-D Symmetric Axis Coordinates: An Overview and Prospectus, 1979.
• Shape Description Using Weighted Symmetric Axis Features, 1978.
• A Geometry for Biology, 1974.
• Biological Shape and Visual Science, 1973.
• Global Brain Function: A Model Using Autonomous Broadcast Elements, 1970.
• Study of the Mathematical Foundations of the Medial Axis Transformation, by Calabi et al., 1968
• A New Model of Global Brain Function, 1967.
• A Transformation for Extracting New Descriptors of Shape, 1964 & 1967.
• Corner and Curvature Discrimination Properties of a Circular Aperture, by G.J. English, 1966.
• Research Directed Toward Pattern Recognition Capabilities of Wave Processes in Active Isotropic Propagating Media, by D.G. Mello & G.J. English, 1966.
• A Mathematical Model of Blum's Theory of Pattern Recognition, by J.C. Kotelly, 1963.
• A Machine for Performing Visual Recognition by Use of Antenna-Propagation Concepts, 1962.
• An Associative Machine for Dealing with the Visual Field and Some of its Biological Implications, 1962.

BibTeX references.

Part 1: Bibliography of the project which ran from Nov.'65 until Aug.'68.

Part 2: A Study of the Skeletal Graph, by L. Calabi

It is shown that:

• Certain shape properties of the silhouette F are easily describable in terms of the skeletal graph G.
• One can study the silhouette F piecemeal by considering each vertex and each edge of G separately.
• The "nearest points map" and its related notions constitute a powerful tool to study geometric properties.

Jump vertex (finite contact):

• Vertex of the skeleton which has more than two points of contact on F (at least one non-degenrate arc of circle).

Skeletal points of order two:

• Contact at two distinct point of F.

Skeletal points of order at least 3:

• The radius function is strictly increasing on at most one branch from that point.

Reconstruction formula, from the skeletal graph, are studied, in terms of the radius function along branches of G. Curvature relationships are studied. Convexity of F in terms of the projected rays (inversive propagation) is studied.

This report is a mathematical investigation of corner and curvature discrimination properties of a small circular aperture that is observing a wave front generated in a continuous isotropic plane by a visual stimulus impinging on the plane. The continuous isotropic plane has the properties of excitation, propagation, and refractory time.

The amplitude function generated by this small aperture is sufficient to completely describe:

• the value of any angle;
• the centers of curvature of arcs, that are segments of the input pattern.

Built two machines, one optical, the other analog-electronic, implementing H.Blum's shape transform (2D grassfire for pattern recognition). These machines are called Pattern Propagation Simulator (PPS) and the Analog-PPS. A summary of the mathematical research done by Calabi et al. is also summarized.

Summary:

Considers the wave (Hyugen's) propagation of Blum in the context of cyclographical (distance) maps.

Propagation rate in a neural net need not be uniform (distance need not be Euclidean), but it should be monotically increasing.

The model of Blum's process allows:

• no flow-through of waves
• a concept of parallel maps
• a graph of relation between the circumference of parallel curves w/r to "distance" form the original pattern
• a pseudo-method for testing symmetry.

BACK

Page created & maintained by Frederic Leymarie, 2000-4.
Comments, suggestions, etc., mail to: leymarie@lems.brown.edu