Histogram equalization is a technique used to enhance the contrast and improve the overall appearance of an image. It redistributes the pixel values in the image's histogram to utilize the entire available dynamic range, thereby stretching the histogram and making the image visually more appealing. The transformation function used in histogram equalization plays a key role in achieving this enhancement. Let's explore histogram equalization and the computation of the transformation function:
Histogram Equalization: Histogram equalization works by mapping the original pixel values to new values that spread across the full range of intensity levels. The process involves the following steps:
- Compute the Histogram: The histogram of an image represents the frequency distribution of pixel values. It is a graphical representation that shows the number of pixels at each intensity level. The histogram is computed by counting the occurrences of each pixel value in the image.
- Compute the Cumulative Distribution Function (CDF): The cumulative distribution function calculates the cumulative sum of the histogram values. It represents the probability of the pixel intensity values being less than or equal to a particular intensity level. The CDF is computed by summing up the histogram values starting from the lowest intensity level to the highest.
- Compute the Transformation Function: The transformation function maps the original pixel values to new values to achieve histogram equalization. It is computed by normalizing the CDF values to span the entire range of intensity levels. The transformation function determines how the original pixel values will be transformed to achieve the desired histogram equalization effect.
- Apply the Transformation: The computed transformation function is applied to each pixel in the image. The original pixel value is replaced with its corresponding transformed value. This remapping redistributes the pixel values in such a way that the histogram is stretched across the full intensity range, enhancing the contrast and improving the image appearance.
Computation of the Transformation Function: The transformation function is computed using the following steps:
- Normalize the CDF: Normalize the CDF values by dividing each value by the total number of pixels in the image. This step ensures that the CDF values are within the range of 0 to 1.
- Scale the Normalized CDF: Multiply the normalized CDF values by the maximum intensity level in the image (e.g., 255 for an 8-bit image) to scale the values to the full range of intensity levels.
- Round the Scaled CDF values: Round the scaled CDF values to the nearest integer to obtain the transformed intensity levels. These rounded values represent the mapping from the original pixel values to the transformed values.
Once the transformation function is computed, it can be applied to each pixel in the image to achieve histogram equalization, resulting in improved contrast and visual quality.
Histogram equalization is a widely used technique in image processing and computer vision applications. It helps overcome issues such as low contrast, poor lighting conditions, or unevenly distributed pixel values, making images visually more appealing and enhancing their interpretability.
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