Which of the following is used for the boundary representation

Answer: Chain codes

Boundary representation (B-rep) describes an object's outline using a sequence of connected boundary elements (pixels or contour points). Chain codes represent the contour by recording the direction of movement between successive boundary pixels (for example, Freeman chain codes).

• Start at a boundary pixel and follow the contour in a consistent direction (clockwise or counterclockwise).

• At each step record the direction to the next boundary pixel (e.g., 0–7 for an 8-connected neighborhood).

• The resulting sequence of direction codes is the chain code; it compactly represents the shape's boundary and can be used for shape analysis and matching.

Why the other listed methods are not the standard boundary representation:

• Quad-tree: Good for hierarchical region partitioning and multi-resolution representation of image areas, but it does not explicitly encode a contour as an ordered sequence.

• Projections: Provide global summaries of pixel distribution along axes (useful for feature extraction), not a detailed contour description.

• Run-length coding: Encodes consecutive identical pixels along scan lines for compression or region representation, not the sequential directions of a boundary.

Advantages of chain codes for boundary representation include compactness, direct encoding of shape information, and suitability for contour-based analysis (with options for normalization to achieve rotation or starting-point invariance).