How to implement sub-pixel linear interpolation in matlab?

The problem is quite clear, but I really don't know where to start.

Assuming this is a gray scale image, the black dot(not the rectangle) is the pixel. For example, x0 is a pixel, it has a x-y location (say (70, 82) ) and a gray value. And I have a direction value(say 135 degree) for pixel x0.

I want to do the linear interpolation along the direction from x0, the method is using the two nearest pixels' gray value. For example, I want to get x's value, the two nearest pixels around x is a and b.

I only want to interpolate pixels on the direction line, and either it's x-coordinate value or y-coordinate value is integer, like the red dots on this picture.

I think my function's input should be a gray scale image, start point x0's coordinate location, a direction value, and a range value to limit how many red dot's I want to get, and output should be the interpolated gray scale values for these red dots.

Thanks for your advices.

Answer 1

[Christiaan]

Dear Sir,

What you could do is defining a starting point in a grid, then draw a line and find all intersections points. Once you have found your point you can use any 1D interpolater to find the corresponding grey points.

A small code that helps you on your way, modified from this question :

The code you can find below:

clc;clear all;close all;

x = 0:5;                            % X-range
y = 0:25;                           % Y-range
lxmb = @(x,mb) mb(1).*x + mb(2);    % Line equation: y = m*x+b
m = 2.7;                              % Slope (or slope array)
b = 1;                              % Intercept (or intercept array)
mb = [m b];                         % Matrix of [slope intercept] values
L1 = lxmb(x,mb);                    % Calculate Line #1 = y(x,m,b)
hix = @(y,mb) [(y-mb(2))./mb(1);  y];   % Calculate horizontal intercepts
vix = @(x,mb) [x;  lxmb(x,mb)];     % Calculate vertical intercepts
hrz = hix(x(2:end),mb)'             % [X Y] Matrix of horizontal intercepts
vrt = vix(y(1:6),mb)'               % [X Y] Matrix of vertical intercepts
figure(1)                           % Draw grids & plot lines
plot(repmat(x,2,length(x)), [0 length(y)-1])    % Vertical gridlines
hold on
plot([0 length(x)-1], repmat(y,2,length(y)))    % Horizontal gridlines
plot(x, L1)                         % Plot more lines here (additional ‘plot’ statements)
hold on
axis equal

hvix = [hrz; vrt];                 % Concatanated ‘hrz’ and ‘vrt’ arrays
srtd = unique(hvix,'rows');        % Remove repeats and sort ascending by ‘x’

plot(srtd(:,1),srtd(:,2),'o');

Good luck! Christiaan

[taa199]

Wow, this is what I am looking for! Thanks!

Answer 2

[Alex Taylor]

Out of curiosity, why not just use interp2 in MATLAB? Just pass in the image and the x,y query points and you are done.