Shape description

The abstraction of shape

Big, small, on its side or upside-down the shape of a fish is the shape of a fish. Shape is a property that is independent of scale, orientation and of position. Shape is an abstraction, a powerful abstraction.

Not only is shape independent of these different properties but it's also robust to occlusion and distortion. Hide chunks of the fish and the shape of the rest is still the same. Skew the fish and the shape is still recognisable - different but recognisable.

Shape is an incredibly powerful property in vision. Shape recognition alone can tell us a huge amount about the content within that image.

Recognising / representing shape

The representation of shape and the recognition of shape are a symbiotic tasks. Understanding the grammar of a language is a powerful leg-up to translating its words. Translating its words lets you better discern the grammar.

So with shape. Shape description is the grammar of this language and the objects themselves - the cats the dogs, guns and laptops, the objects are the words. With a good grammar we're half way there.

My research

My work was concentrated entirely on the problem of shape grammar. I wanted to produce a grammar for shape that reflected its underlying nature. Translate any given shape into this language and immediately the words themselves become more obvious.

Two years into my work and I had gotten to the stage of developing this basic grammar but not building the recognition algorithms that must be layered on top.

Describing the properties of this representation in detail is not something I'm going to do here but it's values were that it was:

• independent of scale
• independent of position
• independent of orientation
• robust to deformation
• robust to occlusion
• low-dimensional

Examples

The two images below shows the representation of a very simple shape, the outline of the letter G.

In the first image, we see a variety of different verions of this shape. No two of them have exactly the same shape and each has a different scale, orientation and position.

Mapping all the shapes into the new shape-space lets us separate the different properties. Having done that, we can very simply map all the instances back onto each other to form a hairy but clearly visible outline of the original letter G (right-hand image).