How to deform 2 circles?

Hello everybody,

[Problem]: I want to deform a circular images to minimize the difference between them.

Original Images:

Currently done:

close all; clc;clear all;
I1 = imread('Image1.png'); I2 = imread('Image2.png');
I = imshowpair(I1, I2, 'montage'); 
I = rgb2gray(I.CData);
bw = im2bw(I);
bw = imfill(imcomplement(bw), 'holes');
imshow(bw);
L = logical(bw);
s = regionprops(L,I, 'Centroid','Area','BoundingBox','MeanIntensity');
%%Smallest cmr index
[min_area_cmr,min_cmr_idx] = min([s.Area]);
min_cmr_bb = s(min_cmr_idx).BoundingBox;
cropped_min_cmr_bb = imcrop(I, min_cmr_bb);
[nr nc] = size(cropped_min_cmr_bb);
%%Background
[~,maxGrayLevel] = max(imhist(I));
[row,col]=ind2sub(size(I), min_cmr_idx);
background_im = I.*0+maxGrayLevel;
%%Intensity
averageMeanIntensity = mean([s.MeanIntensity]);

resized_cmrs =  background_im;
figure(1)
for k = 1 : size(s, 1)
    thisBlobsBoundingBox = s(k).BoundingBox;
    subImage = imcrop(I, thisBlobsBoundingBox);
    subImage = imresize(subImage, [nr,nc]); %re-sized to smallest

      subplot(1, 3, k);
      new_I2(:,:,k)= subImage;
      imshow(new_I2(:,:,k),[]);

      r1 = floor(s(k).Centroid(2)-nr/2);c1 = floor(s(k).Centroid(1) - nc/2);
      r2 = nr + r1- 1; c2 = nc + c1 - 1;

      binaryImage = im2bw(subImage);
      binaryImage = imfill(binaryImage, 'holes');
      mask = bwareaopen(binaryImage, floor(min_area_cmr*0.9));
      subImage = double(subImage) * averageMeanIntensity/s(k).MeanIntensity;
      subImage(~mask) = maxGrayLevel;

      resized_cmr(r1:r2,c1:c2) = subImage;

end

[optimizer,metric] = imregconfig('multimodal');
tformmovingRegisteredDefault = imregister(new_I2(:,:,1), new_I2(:,:,2), 'affine', optimizer, metric);

figure(1); subplot(1, 3, 3); imshowpair(tformmovingRegisteredDefault, new_I2(:,:,2))
title('Default registration')

Wanted Output: And I want to deform one of the images in order to minimize the difference between them. Could you suggest me please any working/implemented techniques in Matlab, please?

@Image Analyst

@Walter Roberson

I'll vote for all your answers and would gladly appreciate any comments.

Ivan