Morphological Image Processing #

Morphological image processing is a technique for analyzing and manipulating shapes in images. It uses transformations based on a defined structure, called a structuring element (SE), to extract geometric and topological information from an image.

Fundamental Operations #

• Dilation: Expands the boundaries of objects by adding pixels.
• Erosion: Shrinks objects by removing pixels from the boundaries.
• Opening: Removes small noise while preserving the shape of larger objects.
• Closing: Fills small holes and gaps in objects.
• Hit-or-Miss: Detects specific patterns in the image by matching structuring elements.

Structuring Elements #

Structuring elements define the shape and size used for morphological operations. Common examples include:

• Squares
• Circles (disks)
• Crosses
• Diamonds

The design of the structuring element is crucial for the success of the operations.

Logical Equivalents in Morphology #

Morphological operations are closely related to set theory and logic:

• Intersection corresponds to logical AND.
• Union corresponds to logical OR.
• Complement corresponds to logical NOT.
• Difference (A - B) corresponds to A AND NOT B.

Applications #

• Boundary Extraction: Detects object boundaries.
• Region Filling: Fills in holes within objects.
• Thinning and Thickening: Refines or emphasizes object boundaries.
• Skeletonization: Reduces objects to their basic structure or skeleton.

Benefits of Morphological Processing #

• Cleans up noisy binary images.
• Analyzes geometric shapes and their relationships.
• Prepares images for advanced tasks such as segmentation and classification.