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Shape FeaturesJamil Ahmad

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Contents• Shape Features• Properties of Shape Features• Shape Descriptor• Descriptors Classification• Simple Shape Features• One-dimensional function for shape representation• Some other shape features• Conclusion• References

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Shape Feature• A prominent attribute or aspect of a shape

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Properties of Shape Features

Efficient shape features must present some essential properties such as:•Identifiability: perceptually similar objects have similar (or the same) features.•Translation, rotation and scale invariance: the location, the rotation and the scaling changing of the shape must not affect the extracted features.

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Properties of Shape Features• Affine invariance: (preserving parallelism and

straightness): shape distortion that preserve shape characteristics should not alter the descriptor.

Noise resistance: features must be as robust as possible against noise, i.e., they must be the same whichever be the strength of the noise in a give range that affects the pattern.

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Properties of Shape Features

• occultation invariance: partial occlusion should not change the descriptor.

• Statistically independent: compact descriptor.• Reliability: as long as one deals with the same

pattern, the extracted features must remain the same.

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Shape Descriptor• Shape Descriptor is a set of numbers that are produced to

represent a given shape feature. A descriptor attempts to quantify the shape in ways that agree with human intuition.

• Usually, the descriptors are in the form of a vector.

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Descriptors Classification• Contour-Based Methods:• Use shape boundary points

• Region-Based Methods:• Use shape interior points

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Simple Shape Features• Some simple geometric features can be used to describe shapes.

Usually, the simple geometric features can only discriminate shapes with large differences; therefore, they are usually used as filters to eliminate false hits or combined with other shape descriptors to discriminate shapes.

• Center of gravity• Eccentricity• Circularity ratio• Rectangularity• Convexity• Solidity• Euler number• Hole area ratio 9

1. Center of Gravity• The center of gravity is also called centroid. Its position should

be fixed in relation to the shape.

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2. Circularity ratio• Circularity ratio represents how a shape is similar to a circle.• Circularity ratio is the ratio of the area of a shape to the

shape's perimeter square:

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3. Rectangularity• Rectangularity represents how rectangular a shape is, i.e.

how much it fills its minimum bounding rectangle:

• where AS is the area of a shape; AR is the area of the minimum bounding rectangle.

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4. Convexity• Convexity is defined as the ratio of perimeters of the

convex hull over that of the original contour.

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5. Solidity• Solidity describes the extent to which the shape is

convex or concave.

• where, As is the area of the shape region and H is the convex hull area of the shape. The solidity of a convex shape is always 1.

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6. Euler number• Euler number describes the relation between the

number of contiguous parts and the number of holes on a shape. Let S be the number of contiguous parts and N be the number of holes on a shape. Then the Euler number is:

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9. Hole area ratio• Hole area ratio HAR is defined as

• where As is the area of a shape and Ah is the total area of all holes in the shape

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One-dimensional function for shape representation• Also known as Shape Signature• It is derived from shape boundary coordinates• The shape signature usually captures the perceptual feature

of the shape• Centroid distance function• Area function• Chord length function

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1. Centroid distance function• The centroid distance function is expressed by the

distance of the boundary points from the centroid of a shape:

• Translation Invariant

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2. Area Function• When the boundary

points change along the shape boundary, the area of the triangle formed by two successive boundary points and the center of gravity also changes. This forms an area function which can be exploited as shape representation.

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3. Chord Length Function• For each boundary point P, its chord length function is the

distance between P and another boundary point P’.

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Some other shape features• Basic Chain Code• Differential Chain Code • Chain Code Histogram• Shape Matrix

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Chain Codes (Basic + Differential• Notation to record a list of boundary bounds along a

contour.• describes the movement along a digital curve or a

sequence of border pixels by using so-called 8-connectivity or 4-connectivity.

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Shape Numbers• To make the chain code rotational invariant, we consider

all cyclic rotations of the differential chain code and choose among them the lexicographically smallest such code. The resulting code is called Shape Number.• Chain Code: • 3 0 0 3 0 1 1 2 1 1 2 3 2

• Differential Chain Code:• 1 0 3 1 1 0 1 3 1 1 3

• Shape Number:• 0 1 3 1 1 3 1 0 3 1 1

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Chain Code Histogram• The CCH reflects the probabilities of different directions

present in a contour.

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Shape Matrix• Shape matrix descriptor is an M × N matrix to represent

a shape region.• Matrix itself is not a feature• Histograms in x- and y-direction• Texture of shape matrix• Frequency analysis

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Conclusion• A shape signature represents a shape by a 1-D function

derived from shape contour.• To obtain the translation invariant property, they are

usually defined by relative values.• To obtain the scale invariant property, normalization is

necessary.• Shape signatures are sensitive to noise, and slight

changes in the boundary can cause large errors in matching procedure.• A shape signature can be simplified by quantizing the

signature into a signature histogram, which is rotationally invariant.

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References• Yang Mingqiang, Kpalma Kidiyo and Ronsin Joseph, “A Survey of Shape

Feature Extraction Techniques” Pattern Recognition Techniques, Technology and Applications, Book edited by: Peng-Yeng Yin, ISBN 978-953-7619-24-4, pp. 626, November 2008, I-Tech, Vienna, Austria

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Thank you

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