Normalizing pixel intensity is the process of transforming the range of pixel values in an image to a new, desired range. This is often done to standardize images for consistent display, processing, or analysis.
One common method involves linear scaling of the original intensity range to the target range.
Understanding Pixel Intensity Normalization
Digital images are composed of pixels, each holding a value representing its intensity or color. These values exist within a specific range, like 0-255 for an 8-bit grayscale image. Normalization maps these original values to a different range, such as 0-1 or another 0-255 range, based on the image's actual minimum and maximum intensity values.
Linear Scaling Method (Min-Max Normalization)
A standard approach to normalize pixel intensity involves adjusting the original range to a new range. This method is often referred to as min-max scaling.
Here are the steps involved, based on the reference provided:
- Determine the Original Range: Find the minimum ($I{\min}$) and maximum ($I{\max}$) pixel intensity values in your image.
- Determine the Desired Range: Define the new minimum ($O{\min}$) and maximum ($O{\max}$) intensity values for your output image (e.g., 0 to 255).
- Shift the Range: Subtract the original minimum ($I{\min}$) from each pixel's intensity value ($P$). This shifts the lowest value to 0, making the new temporary range from 0 to ($I{\max} - I_{\min}$).
- New Pixel Value (Step 1) = $P - I_{\min}$
- Based on the reference example, if the original range is 50 to 180, subtracting 50 from each pixel shifts the range to 0 to (180 - 50) = 0 to 130. The reference states this specifically: subtracting 50 from each of pixel intensity, making the range 0 to 130.
- Scale the Range: Multiply the result from Step 3 by a scaling factor. This factor is the ratio of the desired range's width ($O{\max} - O{\min}$) to the original range's width ($I{\max} - I{\min}$). This scales the values to fit within the target range width.
- Scaling Factor = $\frac{O{\max} - O{\min}}{I{\max} - I{\min}}$
- Final Normalized Pixel Value ($P{norm}$) = $(P - I{\min}) \times \frac{O{\max} - O{\min}}{I{\max} - I{\min}} + O_{\min}$
- Continuing with the reference example, the original range width is 130 (180 - 50), and the desired range width is 255 (255 - 0). The scaling factor is 255/130. The reference states: Then each pixel intensity is multiplied by 255/130, making the range 0 to 255. Note: The reference implicitly assumes $O{\min}$ is 0 in the scaling step, adding $O{\min}$ at the end is needed for a general formula if the target minimum isn't 0. For the 0-255 case shown, adding $O_{\min}$ (0) doesn't change the result.
Example Steps (Based on Reference)
Let's use the example provided in the reference:
- Original Range: 50 to 180
- Desired Range: 0 to 255
| Step | Calculation | Effect on Range | Reference Quote |
|---|---|---|---|
| 1. Shift Minimum to 0 | Subtract original minimum (50) from pixel P | 0 to (180-50) | subtracting 50 from each of pixel intensity, making the range 0 to 130. |
| 2. Scale to New Maximum | Multiply by (255 / (180-50)) = 255/130 | 0 to 255 | Then each pixel intensity is multiplied by 255/130, making the range 0 to 255. |
So, for an individual pixel with intensity $P$:
$P_{norm} = (P - 50) \times \frac{255}{130}$
This method ensures that the pixel with the original minimum intensity maps to the new minimum, the pixel with the original maximum intensity maps to the new maximum, and all values in between are linearly distributed across the new range.
