Mathematical morphology is a theory and technique in image processing that deals with the shape and structure of objects within images. It was introduced by Georges Matheron and Jean Serra in the 1960s. The primary purpose of mathematical morphology is to analyze and manipulate geometric structures within images.
The basic operations in mathematical morphology are dilation and erosion, which are applied using structuring elements (also known as kernels or masks). These operations can be combined to perform more complex operations like opening, closing, and morphological gradient. Here's a brief explanation of some key concepts:
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Dilation: Dilation is an operation that expands the boundaries of objects in an image. It is performed by placing the structuring element at each pixel in the image and setting the value of the pixel to the maximum value within the neighborhood defined by the structuring element.
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Erosion: Erosion is an operation that shrinks the boundaries of objects in an image. It is performed by placing the structuring element at each pixel in the image and setting the value of the pixel to the minimum value within the neighborhood defined by the structuring element.
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Opening: Opening is a combination of erosion followed by dilation. It is useful for removing small objects, smoothing, and separating objects that are close to each other.
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Closing: Closing is a combination of dilation followed by erosion. It is useful for closing small gaps, connecting objects, and smoothing object contours.
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Morphological Gradient: The morphological gradient is the difference between the dilation and erosion of an image. It highlights the boundaries of objects in the image.
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Structuring Element: The structuring element is a small shape or pattern used in dilation and erosion operations. It defines the neighborhood around each pixel that is considered during the operation. Mathematical morphology is widely used in image processing tasks such as noise reduction, object detection, image segmentation, and feature extraction. It provides a powerful set of tools for analyzing and manipulating the structure of images based on the spatial arrangement of pixel values.
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