Explain Color Image Smoothing and Sharpening. How are these operations extended from grayscale to full-color images?

Color image smoothing and sharpening are spatial filtering techniques used to improve image quality by either removing noise (smoothing) or highlighting edges and details (sharpening).

Unlike simple pixel-wise transformations, these techniques use neighboring pixel information to modify each pixel’s value. In full-color images (e.g., RGB), each pixel is a vector with multiple components.


Color Image Smoothing

Definition:

Smoothing reduces image noise and softens fine details. It is done by averaging neighboring pixels.

Method:

We apply a spatial averaging filter (e.g., a box filter or mean filter) over a neighborhood around each pixel.

In grayscale images, smoothing is done as:

It follows from Eq. (6-37) and the properties of vector addition that

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