Combining detail scales of different images

I have created a series of high pass filters of different standard deviations, and I am looking for a way to combine them to maintain the small scale detail of the low sdevs, and the large scale detail of the high sdevs. Currently I am just using a sum with this code:

clear
clc

a=imread('avg.tif');
a=double(a);

[m,n]=size(a);

sdevs=linspace(.4,40,30);

for i=1:length(sdevs)
    filtj=imgaussfilt(a,sdevs(i));
    b{i}=a-filtj;
end 

S=0;
for k=1:length(sdevs)
   S=S+b{k};  
end

c=1.1*S+.4*a;

clearvars b

imshow(c,[0 39000])

[KALYAN ACHARJYA]

Sorry, I didnot get the question. If you can elaborate more (Mathematical), it would be easy to answer.

[Bray Falls]

So I have performed a set of gaussian low pass filters on one target image, and subtracted each from the target image to obtain a set of high pass filters, each enhancing detail of a particular scale. I want to integrate the high pass filters so that the structures in the smallest scale filter don't get washed out by the enhancements made in the large scale filters.

I have attempted performing just a simple sum of the set of filters, but it washed out the smaller details quite a bit.

[Subhadeep Koley]

From my understanding you only want to boost the high frequency "detail" components without affecting the low frequency "approximation" components right ?

Answer 1

[Kavya Vuriti]

Hi,

Instead of using simple sum, you can try using weighted summation. The images obtained from small scale filters can be given higher weights so that the structures in the small-scale filter doesn’t get washed out.