Image Enhancement

For linear contrast stretching, we use the following formula: Where:
- (the input DN value),
- (the minimum DN value),
- (the maximum DN value),
- (the maximum possible value for 8-bit data),
- (the minimum possible value for 8-bit data).
Substituting the values into the formula: Final Answer:

To answer this question, we need to understand what each filter does and how it relates to the given kernels (P, Q, R, S). Filters are used in image processing for operations like edge detection, smoothing, and enhancing details. Here, we are given four types of filters and their respective kernels. Let's analyze each one: - (I) Low Frequency Filter (P): This filter is designed to smooth an image by removing high-frequency noise, which represents rapid intensity changes in the image. The kernel for a low frequency filter typically contains values that help to average or blur the image. The kernel is a smooth, symmetric kernel with positive values that would result in averaging the neighboring pixels. - (II) High Frequency Filter (Q): High-frequency filters emphasize rapid changes in pixel values, such as edges. These filters are often used for edge detection. The kernel is a difference kernel, with positive and negative values, which emphasizes the differences between adjacent pixels, highlighting edges. - (III) Laplacian Filter (R): The Laplacian filter is used for edge detection and image enhancement by detecting areas of rapid intensity change. The kernel contains both positive and negative values, which helps to highlight rapid changes in intensity, characteristic of the Laplacian filter. - (IV) Sobel Operator Filter (S): The Sobel operator is used for edge detection and enhances the gradient of an image. It helps in detecting edges by calculating the gradient of image intensity. The kernel is the standard Sobel operator kernel, which is used for edge detection in both horizontal and vertical directions. Matching the Filters to the Kernels:
- (I) Low Frequency Filter (P): The kernel is a smooth kernel, which is ideal for low-frequency filtering, and corresponds to the low-frequency filter. - (II) High Frequency Filter (Q): The kernel is a difference-based kernel, which corresponds to the high-frequency filter. - (III) Laplacian Filter (R): The kernel is a Laplacian kernel, which is used to highlight rapid changes, thus matching the Laplacian filter. - (IV) Sobel Operator Filter (S): The kernel is the Sobel operator, which is specifically designed for edge detection, matching the Sobel operator filter. Thus, the correct matches are: - (I) - P (Low Frequency Filter) - (IV) - Q (Sobel Operator Filter) Hence, the correct answer is (C) I - P and IV - Q.

When the histogram of an image is non-Gaussian, piece-wise linear contrast stretching is preferred. This technique divides the image histogram into several intervals and applies different stretching to each interval. This allows for better contrast enhancement in non-uniform histograms.
Step 1: Understanding Contrast Stretching
- Option (A) is correct because piece-wise linear contrast stretching is specifically useful when the histogram is non-Gaussian, allowing for better control over various ranges of pixel values.
- Option (B) refers to min-max linear contrast stretching, which is used for images with uniform histograms, not typically for non-Gaussian images.
- Option (C) refers to percentage linear contrast stretching, which is not commonly used in non-Gaussian histogram enhancement.
- Option (D) refers to standard deviation contrast stretching, which is also not ideal for non-Gaussian histograms. Step 2: Conclusion
The preferred method for non-Gaussian histograms is (A) Piece-wise Linear Contrast Stretching.