illustrate fspecial function for linear motion blur

I am trying illustrate fspecial('motion',x,y) function In help of mathlab I see the guide for creating kernel 1. Construct an ideal line segment with the desired length and angle, centered at the center coefficient of h. 2. For each coefficient location (i,j), compute the nearest distance between that location and the ideal line segment. 3. h = max(1 - nearest_distance, 0); 4. Normalize h:h = h/(sum(h(:))); example: fspecial('motion',3,45) I describe like this 2. a = [sqrt(2) sqrt(2)/2 0; sqrt(2)/2 0 sqrt(2)/2; 0 sqrt(2)/2 sqrt(2);] 3. h = max(1-a,0); 4. h = h/(sum(h(:)))

and the result is: 0 0.0702 0.2397 0.0702 0.2397 0.0702 0.2397 0.0702 0 but using fspecial('motion',3,45) the result is 0 0.0754 0.1883 0.0754 0.3215 0.0754 0.1883 0.0754 0 Please tell me where am I wrong ? What is the kernel of linear motion blur in fspecial function? Thanks.

Answer 1

[Keqi Ma]

Following is the code for 'motion' kernel in Matlab. There is no max opearation at all. You can follow this code to understand the 'motion' kernel.

len = max(1,p2);

half = (len-1)/2;% rotate half length around center

phi = mod(p3,180)/180*pi;

cosphi = cos(phi);

sinphi = sin(phi);

xsign = sign(cosphi);

linewdt = 1;

% define mesh for the half matrix, eps takes care of the right size

% for 0 & 90 rotation

sx = fix(half*cosphi + linewdt*xsign - len*eps);

sy = fix(half*sinphi + linewdt - len*eps);

[x y] = meshgrid(0:xsign:sx, 0:sy);

% define shortest distance from a pixel to the rotated line

dist2line = (y*cosphi-x*sinphi);% distance perpendicular to the line

rad = sqrt(x.^2 + y.^2);

% find points beyond the line's end-point but within the line width

lastpix = find((rad >= half)&(abs(dist2line)<=linewdt));

%distance to the line's end-point parallel to the line

x2lastpix = half - abs((x(lastpix) + dist2line(lastpix)*sinphi)/cosphi);

dist2line(lastpix) = sqrt(dist2line(lastpix).^2 + x2lastpix.^2);

dist2line = linewdt + eps - abs(dist2line);

dist2line(dist2line<0) = 0;% zero out anything beyond line width

% unfold half-matrix to the full size

h = rot90(dist2line,2);

h(end+(1:end)-1,end+(1:end)-1) = dist2line;

h = h./(sum(h(:)) + eps*len*len);

if cosphi>0,

h = flipud(h);

end