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The procedure for performing histogram matching using a normal distribution as a reference involves the following steps:

1. Calculate the mean and standard deviation of the reference normal distribution.

2. Calculate the mean and standard deviation of the target image.

3. Create a cumulative distribution function (CDF) for the reference normal distribution using the mean and standard deviation calculated in the first step.

4. Create a CDF for the target image using the mean and standard deviation calculated in the second step.

5. For each pixel value in the target image, find the corresponding pixel value in the reference CDF such that the two distributions match. This can be done by finding the closest value in the reference CDF to the target CDF.

6. Replace the pixel value in the target image with the corresponding pixel value from the reference distribution.

7. Repeat steps 5 and 6 for all pixel values in the target image.

8. The result is a new image with the same histogram shape as the reference normal distribution.