Boundary Extraction, Chain Code Generation, Differential Chain Code, and Frequency Vector Generation Program

Boundary extraction is a crucial step in image processing, used to obtain object contours from binary images. This is typically implemented using edge detection algorithms or tracing algorithms, such as Sobel operator or Canny edge detection. The extracted boundary consists of a series of continuous pixels that can be used for further processing. In MATLAB implementation, the `bwboundaries` function can be employed to extract boundary coordinates from binary images, returning a cell array containing coordinate sequences for each detected object.

Chain code generation is the process of converting boundary point sequences into chain code representation. Chain code is an encoding method that describes object contours by recording directional changes between boundary points, effectively reducing data volume. Common chain codes include 4-direction and 8-direction variants, with 8-direction chain code being more precise as it can describe more directional variations. The implementation typically involves calculating the direction between consecutive boundary points using directional vectors and mapping them to predefined code values (0-7 for 8-direction chain code).

Differential chain code generation enhances rotation invariance. Since ordinary chain codes change when objects rotate, differential chain code eliminates rotational effects by computing differences between adjacent chain codes. This is achieved by subtracting each element from its predecessor in the original chain code and applying modulo operation to the results, ensuring consistent differential chain codes after rotation. The MATLAB implementation would use `mod(diff(chain_code), 8)` to compute these differences while maintaining circular continuity.

Frequency vector generation involves statistical analysis of differential chain codes by calculating the frequency of each direction occurrence. This step facilitates feature extraction, enabling shape differentiation based on directional distributions. Frequency vectors exhibit excellent rotation invariance, making them suitable for image matching and classification tasks. The implementation typically uses histogram computation with `histcounts` function in MATLAB to count occurrences of each direction code (0-7), then normalizes the counts to create rotation-invariant feature vectors.

When implementing these steps in MATLAB, built-in functions like `bwboundaries` can be used for boundary extraction, while custom code should be written for chain code, differential chain code, and frequency vector calculations to ensure rotation-invariant features. These methods find widespread applications in shape recognition, object classification, and computer vision systems where rotation-independent shape descriptors are essential.