Follow two steps:

1. Build the edge map from your image.

2. Compare PSNR and SSIM for the edge map.

This is very simple. Subtract the original image from the enhanced image, then you will find what you have enhanced. if you got only edges and are sharped its mean you did it.

In my opinion, you can compare the result of your developed method with the results of the other classical methods like Canny, LoG and so on... But in order to get a metric evaluation, having a solid edges with a minimal number of noisy halls or distortions (in other words, extracted edges that approximate the real edges in the original image) may represent a natural and simple way...

As you can determine and compare the SNR between different images

Follow two steps:

1. Build the edge map from your image.

2. Compare PSNR and SSIM for the edge map.

Thanks guys. But, again PSNR and SSIM are mainly for image quality evaluation and not for measuring improvement of strength of edges. Because, I compared Nyul normalization against my method and even with less SSIM score, my method is giving good segmentation results.

It would be better if you show some examples of your results in order to make your question clearer in this case ..

You can use structural similarity SSIM index to evaluate your proposed algo. You can also compare your results with classical edge detector like - sobel, canny, LoG etc..

Use the DWT based Unsharp masking for Edge enhancement along with the Laplacian filtering technique .

Compare the result with the Sobelle filtering technique.You will find that Laplacian technique is better.

Many specialized metrics exist for such purpose, including:

1- sharpness index (S)

Leclaire, A., & Moisan, L. (2015). No-reference image quality assessment and blind deblurring with sharpness metrics exploiting Fourier phase information. Journal of Mathematical Imaging and Vision, 52(1), 145-172.

2-Cumulative Probability of Blur Detection (CPBD)

N. D. Narvekar and L. J. Karam, "A No-Reference Image Blur Metric Based on the Cumulative Probability of Blur Detection (CPBD)," IEEE Transactions on Image Processing, 2011.

1. Apply different edge detectors to original and your edge enhanced images.

2. Find no. of connected components to all the images.

if your edge enhanced image has more no. of connected components, then you can show that your image has more edges

the following link may be useful, if you have ground truth images for your inputs

https://in.mathworks.com/matlabcentral/fileexchange/52205-measures-of-edge-detection