# Broadcasting

- Time
- 25 minutes
- Activity
- Demo/Discussion

By this point we're hopefully all pretty familiar with Octave code that looks like

```
A=[1,2,3;
4,5,6];
B=A.*2
```

We're also familiar with

```
C=A .* [2,2,2; 2,2,2]
```

It turns out these are actually the same operation, since Octave converts the first into the second via broadcasting.

Quoting from the Octave docs, for elementwise binary operators and functions

The rule is that corresponding array dimensions must either be equal, or one of them must be 1.

In the case where one if the dimensions is `1`

, the smaller matrix is
*tiled* to match the dimensions of the larger matrix.

Here's another example you can try.

```
x = [1 2 3;
4 5 6;
7 8 9];
y = [10 20 30];
x + y
```

## Reshaping arrays

One potentially surprising aspect of Octave arrays is that the number
of dimensions is independent from the number of elements. We can add
as many dimensions as we like, as long as the only possible index in
those dimensions is `1`

. This can be particularly useful when trying
to broadcast with higher dimensional arrays.

```
ones(3,3,3) .* reshape([1,2,3],[1,1,3])
ones(3,3,3) .* reshape([1,2,3],[1,3,1])
```

# Scaling layers of arrays

- Time
- 25 minutes
- Activity
- Small Groups

Complete the following function. You may want to copy the definitions of `A`

and `B`

into the REPL
to understand the use of `cat`

.

```
## usage: scale_layers(array, weights)
##
## multiply each layer of a 3D array by the corresponding weight
function out = scale_layers(array, weights)
out =
endfunction
%!test
%! onez = ones(3,3);
%! A=cat(3,onez, 2*onez, 3*onez);
%! B=cat(3,onez, 6*onez, 15*onez);
%! assert(scale_layers(A,[1;3;5]),B)
```

## Scaling a colour channel

Save the image above left as `~/fcshome/teaching/cs2613/labs/L23/paris.jpg`

Run the following demo code; you can change the weight vector for different colourization.

```
paris=imread("paris.jpg");
sepia=scale_layers(paris,[0.9,0.62,0.34]);
imshow(sepia);
```

You should get something like the following

# Converting to monochrome

- Time
- 25 minutes
- Activity
- Small Groups

Either for creative reasons, or as part of a more complex image processing task, it is common to convert images to monochrome.

Save the following image as
`~/fcshome/teaching/cs2613/labs/L23/paris.jpg`

Complete the following function using `scale_layers`

.

```
function out = monochrome(in, weights=[0.21,0.72,0.07])
out =
endfunction
```

Run the `monochrome`

function on `owl.jpg`

, you should get something like the following.

Try a few different values of weight vectors, see if you can generalize some rules from your experiments.

# Gradient

- Time
- 25 minutes
- Activity
- Small Groups

One useful operation on images is to detect how they are changing
locally. Roughly speaking the *gradient* can be thought about as
specifying both *how much* the intensity is chanaging, and what
direction that change is happening in. Octave returns that
information as an `(x,y)`

vector in the usual parallel array way.

```
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];
[Dx, Dy] = gradient(A);
imshow(A);
figure;
imshow(Dx);
figure;
imshow(Dy);
```

Complete the follow function, by combining the `Dx`

and `Dy`

arrays
into a single array with the norm of the vector. The demo should
produce an image somewhat like the one below.

```
function normimg = normgrad(img)
[Dx, Dy] = gradient(img);
normimg =
endfunction
%!demo
%! owl=imread("owl.jpg");
%! monowl=monochrome(owl);
%! ng = normgrad(monowl);
%! imshow(ng*2, [0,20]);
```