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OBJECT RECOGNITION – BLOB ANALYSIS

OBJECT RECOGNITION – BLOB ANALYSIS. Examples of form parameters that are invariant with respect to position, orientation, and scale: Number of holes in the object Compactness or Complexity: (Perimeter) 2 /Area Moment invariants

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OBJECT RECOGNITION – BLOB ANALYSIS

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  1. OBJECT RECOGNITION – BLOB ANALYSIS • Examples of form parameters that are invariant with respect to position, orientation, and scale: • Number of holes in the object • Compactness or Complexity: (Perimeter)2/Area • Moment invariants • All of these parameters can be evaluated during contour following.

  2. GENERALIZED MOMENTS • Shape features or form parameters provide a high level description of objects or regions in an image • Many shape features can be conveniently represented in terms of moments. The (p,q)th moment of a region R defined by the function f(x,y) is given by:

  3. GENERALIZED MOMENTS • In the case of a digital image of size n by m pixels, this equation simplifies to: • For binary images the function f(x,y) takes a value of 1 for pixels belonging to class “object” and “0” for class “background”.

  4. GENERALIZED MOMENTS X 7 Area 33 20 159 Moment of Inertia 64 93 Y

  5. SOME USEFUL MOMENTS • The center of mass of a region can be defined in terms of generalized moments as follows:

  6. SOME USEFUL MOMENTS • The principal axis of an object is the axis passing through the center of mass which yields the minimum moment of inertia. • This axis forms an angle θ with respect to the X axis. • The principal axis is useful in robotics for determining the orientation of randomly placed objects.

  7. Principal Axis: Derivation

  8. Example X Principal Axis Center of Mass Y

  9. SOME USEFUL MOMENTS • The moments of inertia relative to the center of mass can be determined by applying the general form of the parallel axis theorem:

  10. SOME (MORE) USEFUL MOMENTS • The minimum/maximum moment of inertia about an axis passing through the center of mass are given by:

  11. SOME (MORE) USEFUL MOMENTS • The following moments are independent of position, orientation, and reflection. They can be used to identify the object in the image.

  12. SOME (MORE) USEFUL MOMENTS • The following moments are normalized with respect to area. They are independent of position, orientation, reflection, and scale.

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