% RegisterFourierMellin
% This code is the result of my messing around with Matlab investigating
% various image registration techniques. I came across the excellent
% (although perhaps a little messy and buggy) fm_gui_v2 from Adam Wilmer
% here:
% http://www.mathworks.com/matlabcentral/fileexchange/loadFile.do?objectId=3000&objectType=file
% Because my needs are essentially the algorithm itself in a neat and tidy
% format to enable an easier conversion to C++, I've extracted what I think
% is the essence of the Fourier Mellin method into this file. Obviously
% I haven't included a GUI. In order to test it, you need to set the first
% two statements to load in 2 image files of the same size, in 8 bit grayscale.
% I took lena and then used Gimp to rotate/shift/crop at various angles.
% It isn't sub-pixel accurate, although I'm aware of methods to achieve
% this by extracting the peaks around the peak of the phase correlation and
% finding the maxima (least squares perhaps).
% The methods towards the end of the program are cribbed directly from
% Adam's version. I'm new to Matlab (been playing with it for less than
% a fortnight), so I wasn't able to get my head around his log polar transform
% or the final "blending" of the two images together.
% I'd like to thank Adam for publishing his version. Without it I'd never
% have known I had to take the log polar transform of the magnitude of the
% FFT, rather than the log polar transform of the original image!
function RegnisterFourierMellin()
% The procedure is as follows (note this does not compute scale)
% (1) Read in I1 - the image to register against
% (2) Read in I2 - the image to register
% (3) Take the FFT of I1, shifting it to center on zero frequency
% (4) Take the FFT of I2, shifting it to center on zero frequency
% (5) Convolve the magnitude of (3) with a high pass filter
% (6) Convolve the magnitude of (4) with a high pass filter
% (7) Transform (5) into log polar space
% (8) Transform (6) into log polar space
% (9) Take the FFT of (7)
% (10) Take the FFT of (8)
% (11) Compute phase correlation of (9) and (10)
% (12) Find the location (x,y) in (11) of the peak of the phase correlation
% (13) Compute angle (360 / Image Y Size) * y from (12)
% (14) Rotate the image from (2) by - angle from (13)
% (15) Rotate the image from (2) by - angle + 180 from (13)
% (16) Take the FFT of (14)
% (17) Take the FFT of (15)
% (18) Compute phase correlation of (3) and (16)
% (19) Compute phase correlation of (3) and (17)
% (20) Find the location (x,y) in (18) of the peak of the phase correlation
% (21) Find the location (x,y) in (19) of the peak of the phase correlation
% (22) If phase peak in (20) > phase peak in (21), (y,x) from (20) is the translation
% (23a) Else (y,x) from (21) is the translation and also:
% (23b) If the angle from (13) < 180, add 180 to it, else subtract 180 from it.
% (24) Tada!
% Requires (ouch):
% 6 x FFT
% 4 x FFT Shift
% 3 x IFFT
% 2 x Log Polar
% 3 x Phase Correlations
% 2 x High Pass Filter
% 2 x Image Rotation
% ---------------------------------------------------------------------
% Load first image (I1)
I1 = imread('lena.bmp');
% Load second image (I2)
I2 = imread('lena_cropped_rotated_shifted.bmp');
% ---------------------------------------------------------------------
% Convert both to FFT, centering on zero frequency component
SizeX = size(I1, 1);
SizeY = size(I1, 2);
FA = fftshift(fft2(I1));
FB = fftshift(fft2(I2));
% Output (FA, FB)
% ---------------------------------------------------------------------
% Convolve the magnitude of the FFT with a high pass filter)
IA = hipass_filter(size(I1, 1),size(I1,2)).*abs(FA);
IB = hipass_filter(size(I2, 1),size(I2,2)).*abs(FB);
% Transform the high passed FFT phase to Log Polar space
L1 = transformImage(IA, SizeX, SizeY, SizeX, SizeY, 'nearest', size(IA) / 2, 'valid');
L2 = transformImage(IB, SizeX, SizeY, SizeX, SizeY, 'nearest', size(IB) / 2, 'valid');
% Convert log polar magnitude spectrum to FFT
THETA_F1 = fft2(L1);
THETA_F2 = fft2(L2);
% Compute cross power spectrum of F1 and F2
a1 = angle(THETA_F1);
a2 = angle(THETA_F2);
THETA_CROSS = exp(i * (a1 - a2));
THETA_PHASE = real(ifft2(THETA_CROSS));
% Find the peak of the phase correlation
THETA_SORTED = sort(THETA_PHASE(:)); % TODO speed-up, we surely don't need to sort
SI = length(THETA_SORTED):-1:(length(THETA_SORTED));
[THETA_X, THETA_Y] = find(THETA_PHASE == THETA_SORTED(SI));
% Compute angle of rotation
DPP = 360 / size(THETA_PHASE, 2);
Theta = DPP * (THETA_Y - 1);
% Output (Theta)
% ---------------------------------------------------------------------
% Rotate image back by theta and theta + 180
R1 = imrotate(I2, -Theta, 'nearest', 'crop');
R2 = imrotate(I2,-(Theta + 180), 'nearest', 'crop');
% Output (R1, R2)
% ---------------------------------------------------------------------
% Take FFT of R1
R1_F2 = fftshift(fft2(R1));
% Compute cross power spectrum of R1_F2 and F2
a1 = angle(FA);
a2 = angle(R1_F2);
R1_F2_CROSS = exp(i * (a1 - a2));
R1_F2_PHASE = real(ifft2(R1_F2_CROSS));
% Output (R1_F2_PHASE)
% ---------------------------------------------------------------------
% Take FFT of R2
R2_F2 = fftshift(fft2(R2));
% Compute cross power spectrum of R2_F2 and F2
a1 = angle(FA);
a2 = angle(R2_F2);
R2_F2_CROSS = exp(i * (a1 - a2));
R2_F2_PHASE = real(ifft2(R2_F2_CROSS));
% Output (R2_F2_PHASE)
% ---------------------------------------------------------------------
% Decide whether to flip 180 or -180 depending on which was the closest
MAX_R1_F2 = max(max(R1_F2_PHASE));
MAX_R2_F2 = max(max(R2_F2_PHASE));
if (MAX_R1_F2 > MAX_R2_F2)
[y, x] = find(R1_F2_PHASE == max(max(R1_F2_PHASE)));
R = R1;
else
[y, x] = find(R2_F2_PHASE == max(max(R2_F2_PHASE)));
if (Theta < 180)
Theta = Theta + 180;
else
Theta = Theta - 180;
end
R = R2;
end
% Output (R, x, y)
% ---------------------------------------------------------------------
% Ensure correct translation by taking from correct edge
Tx = x - 1;
Ty = y - 1;
if (x > (size(I1, 1) / 2))
Tx = Tx - size(I1, 1);
end
if (y > (size(I1, 2) / 2))
Ty = Ty - size(I1, 2);
end
% Output (Sx, Sy)
% ---------------------------------------------------------------------
% FOLLOWING CODE TAKEN DIRECTLY FROM fm_gui_v2
% Combine original and registered images
input2_rectified = R; move_ht = Ty; move_wd = Tx;
total_height = max(size(I1,1),(abs(move_ht)+size(input2_rectified,1)));
total_width = max(size(I1,2),(abs(move_wd)+size(input2_recti
评论1
最新资源