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

Boundary extraction, chain code generation, and related processing techniques are commonly used contour analysis methods in image processing, primarily employed to describe and identify object shape features. These methods can achieve efficient computation and processing in MATLAB while also generating rotation-invariant feature descriptors through differential chain codes and frequency vectors.

In image processing, boundary extraction is the initial step. Using edge detection algorithms such as Sobel, Canny, or simple threshold segmentation, we can extract contour point sets of objects from the original image. These contour points are typically arranged in clockwise or counterclockwise order, preparing for subsequent chain code generation.

During chain code generation, we adopt Freeman chain code's 8-direction encoding scheme, using digits 0-7 to represent movement directions from the current pixel to the next pixel. This representation effectively compresses contour information, but directly generated chain codes are highly sensitive to object rotation. To enhance rotation invariance, we introduce the concept of differential chain codes. Differential chain codes describe contours by calculating the change between adjacent direction codes, ensuring that when an object rotates, although the original chain code changes entirely, the relative relationships in the differential chain code remain unchanged.

Frequency vector generation is another rotation-invariant feature representation method. We count the frequency of each direction occurrence in the chain code and normalize them to form a feature vector. Although this method loses directional sequence information, it provides complete rotation invariance and offers simple, efficient computation. In practical applications, combining differential chain codes and frequency vectors can create more robust shape description features.

When implementing these algorithms in MATLAB, we can leverage its powerful matrix operations and image processing toolbox functions. For chain code processing, special attention must be paid to boundary conditions and contour closure handling. Differential chain code computation can utilize modulo-8 arithmetic to ensure result correctness. Frequency vector statistics can be directly implemented using histogram functions or accumulators.