General Intelligence :

Classification of 1D Shapes

Here I attempt to classify all 1D shapes (contours) into primitive elements (lines, curves, junctions).

My view is that the vision problem (especially the recognition of 3D objects) can be solved via a 3D → 2D → 1D process. All 3D objects can be defined by 2D elements (surfaces), and all 2D shapes (areas) can be defined by 1D contours.

Main Classes

All 1D shapes can be decomposed into:

Properties: (thickness, color, texture)

1. Straight Lines

Properties: (position, length, orientation, end points)

2. Curves

4 subtypes:

1. Simple Curves

Curves with no inflections:

Properties: (position, length, orientation, end points, curvature)

2. Ellipses/Circles

Properties: (position, orientation, size, axes ratio)

3. Complex Curves

Properties: (position, length, end points, # of inflections, curvatures)

4. Complex Loops

Properties: (position, area, shape description, # of inflections)

3. Junctions

Properties: (position, # of lines, angles)

3 subtypes:

1. L

2. T

3. Y

4. X

May have >4 lines of convergence.

Examples

The following examples illustrate the concept of self-aggregation, which means edgel detectors (or "neurons") aggregating with others with similar attributes such as color, orientation, etc.

A line with a slight bend: (the bending is noticed even though it is very slight, because the A & B parts are very straight in contrast):

This line has many bends but is still recognized as a continuous line:

For the following line, a simple algorithm may classify it as a curve, but people will describe it as: two slightly curved lines A & C, bending at a point B. This illustrates the context-dependent aspect of human vision.

The following is yet another context-dependent example: we see 2 "shaky" but straight lines bending at an angle.

What is a "straight" line is relative: B is straighter than A but in the above context A is also considered a straight line.

People will describe the following as a regular "sine" curve:

This is also a simple curve that people can describe with basic features such as crest and trough and being smooth:

People can also characterize line junctions with special attributes, eg a "smooth" junction:

This can be considered as 1 line with 2 colors:

This is also considered a simple curve with internal texture:

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18/Mar/2006 (C) General intelligence corporation limited