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Gaussian smoothing is 2D operator and is a spatial domain smoothing technique. It uses a kernel that represents the shape of a Gaussian (`bell-shaped') hump.
2-D Gaussian distribution with mean (0,0) and 𝞂=1
The standard deviation, σ determines the width of the filter and hence the amount of smoothing. A filter with a large σ will suppress much of the noise, but also smooth away the weakest edges
Kernel used :
[ 0.0947 0.1183 0.0947
0.1183 0.1478 0.1183
0.0947 0.1183 0.0947 ]
Example smoothed image :
The Structural Similarity Index (SSIM) : Perceptual metric that quantifies image quality degradation
➢ It outputs the similarity of the given image with respect to reference image (assumed to be of perfect quality) .
➢ Considered to be an apt measure of image quality than traditional Peak-Signal-to-Noise Ratio (PSNR) and Mean Squared Error (MSE) as it takes into account the structural information than just absolute errors.
Structural information is more relevant to images as spatial distribution of pixels holds a strong amount of information about the image.
If both the images are exactly similar, SSIM = 1 else will be less than 1
Result expected when using different multipliers :
➢ Depends on the image considered. SSIM evaluated pixelwise.
➢ Approximate multiplier with truncation deviates more from the outputs of Exact/Dadda multiplier, compared to approximated multiplier w/o truncation. Thus the Gaussian Smoothing that uses Approx. mul with truncation should be more structurally dissimilar thus a lower SSIM value.
➢ I.e., (SSIM)Approx. Mul with truncation < (SSIM)Approx. Mul without truncation
Results obtained using the designed approximate multipliers :
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