Convolution and smoothing I

In order to smooth out some of the noise (or just isolated bright pixels), we can replace the value of each pixel with a weighted average of it's neighbourhood. The simplest approach is the so called box blur, where each pixel in the neighbourhood is added up, and the result divided by the number of pixels. The Octave function conv2(A,B) provides an easy way to apply a convolution or kernel to a matrix. This just means that B specifies the weights in averaging the neighbourhood.

Fill in the appropriate matrix (formula) B to make the following smoothing demo work.

A = [0,0,0,0,0,1;
     0,1,1,1,0,0;
     0,1,1,1,0,1;
     0,1,1,1,1,0;
     0,1,1,1,1,0;
     0,0,0,0,0,0];


for j=2:12
  B=
  AB = conv2(A,B);
  imshow(AB,[]);
  pause(1);
endfor

As the variable j increases, the images should look smoother but also less detailed.

Convolution and Smoothing II

Generalize the demo above to make a smoothing function. For variety we're going to use the Paris image image from a previous lab for the demo.

function S=smooth(in, side=3)
    S =
endfunction

%!test
%! A = [0,0,0,1;
%!      1,1,0,0;
%!      1,1,0,1;
%!      1,1,1,0];
%! B= [0.50, 0.25, 0.25, 0.25;
%!     1.00, 0.50, 0.25, 0.25;
%!     1.00, 0.75, 0.50, 0.25;
%!     0.50, 0.50, 0.25, 0.00];
%! assert(smooth(A,2),B,eps);

%!demo
%! paris=imread("paris.jpg");
%! monoparis=monochrome(paris,[1/3,1/3,1/3]);
%! imshow(monoparis,[])
%! pause(1);
%! imshow(smooth(monoparis),[])
%! pause(1);
%! imshow(smooth(monoparis,10),[])
%! pause(1);
%! imshow(smooth(monoparis,20),[])

Use your new function to complete the following script. Adjust the smoothing and threshold parameters to approximate the image below. You will need to download the leaf image from last lab.

leaf=imread("leaf.jpg");
monoleaf=monochrome(leaf);
smoothed=
ng = normgrad(smoothed)
[rows, cols] =

clf
hold on;
imshow(leaf,[]);
plot(cols,rows,".","markersize",1);

Smoothing and gradient via convolution

As you probably saw, the second argument to conv2 can be much more general than just uniform weights. In particular some of the weights can be negative, e.g. to approximate a gradient calculation.

One example is the Soebel Operator which combines gradiant and smoothing operations.

Refering to the Wikipedia page, complete the function to calculuate the Soebel operator. You will also need to define function norm2, which can be copied from the definition of normgrad (without the gradient part).

function [Gx,Gy]=soebel(in)


  Gx =
  Gy =
endfunction

%!demo
%! leaf=imread("leaf.jpg");
%! monoleaf=monochrome(leaf);
%! [Dx, Dy] = soebel(monoleaf);
%! ns = norm2(Dx,Dy);
%! [rows,cols] = threshold(ns,150);
%! clf
%! hold on
%! imshow(leaf);
%! plot(cols,rows,".","markersize",10);

In the resulting figure the size of the detected pixels is exaggerated to make them easier to spot.

Before next lab