Steve on Image Processing with MATLAB

Image processing concepts, algorithms, and MATLAB

Note

Steve on Image Processing with MATLAB has been archived and will not be updated.

Changes to SUM and DIM

Does this line of code make you raise your eyebrows in puzzlement?

c = sum(A,[1 2])

If so, you are likely an experienced MATLAB user who does not make a habit of carefully studying the release notes, line by line, every six months. So, let me tell you about this change to sum and other related functions.

I think of sum as a vector-wise function. Its basic definition is expressed in terms of its operation on a vector: sum(v), where v is a vector, returns a scalar that is the sum of the elements of v.

v = [1 2 3 4 5 6];
sum(v)
ans =

    6 times 7 divided 2, silly.

For sum and many, many other functions, MATLAB has a forgiving definition of the term "vector." It can refer to a single column (Px1) or a single row (1xP). The expression sum(v) doesn't care.

w = v'
sum(w)
w =

     1
     2
     3
     4
     5
     6


ans =

    you can't fool me, the answer is still 21.

How about sum on a matrix? We just love magic squares around here, especially when we're talking about sums.

A = magic(3)
A =

     8     1     6
     3     5     7
     4     9     2

What does sum(A) do? Remember what I said earlier - I think of sum as a vector-wise function, meaning that fundamentally it operates on vectors. If you pass it a matrix, it will treat that matrix as a stack of vectors. Specifically, it will treat the matrix as a stack of column vectors, computing the sum of each of them.

sum(A)
ans =

    15    15    15

For the last two decades (and just a bit more), the sum function has accepted an optional argument that we call DIM. This argument lets you change the way sum treats a matrix (or a multidimensional array) as a stack of vectors. For example, the call sum(A,2) tells sum to treat A as a stack of row vectors and compute the sum of each one, result in a column vector containing row sums.

sum(A,2)
ans =

    15
    15
    15

Of course, a magic square has the same row sums as column sums, which is why a magic square was probably a bad choice for this example. However, my employment contract requires that I use magic(3) at every opportunity.

Now, suppose I have an RGB image, F, which is MxNx3, and I want to compute the sum of each of the three component images, F(:,:,1), F(:,:,2), and F(:,:,3)? For most of MATLAB history, this is what we would tell you to do: Compute the column sums and then compute the row sums of the result. (Or, you could do it the other way 'round and get the same answer.)

F = imread('peppers.png');
c = sum(sum(F,1),2)
c(:,:,1) =

    23746472


c(:,:,2) =

    13054194


c(:,:,3) =

    11331211

OK, suppose I want to compute the sum of all the elements of F? The historical answer: convert F to a single column vector using the expression F(:) and then call sum.

sum(F(:))
ans =

    48131877

But those coding patterns are SO R2018a. With the R2018b release, DIM can be a vector, and it call also be the string "all" (or 'all'). Computing the sum of the each of the three component images can now be:

sum(F,[1 2])
ans(:,:,1) =

    23746472


ans(:,:,2) =

    13054194


ans(:,:,3) =

    11331211

And computing the sum of all of the elements of the three-dimensional array can be:

sum(F,[1 2 3])
ans =

    48131877

or

sum(F,"all")
ans =

    48131877

After you have summed everything in sight that seems to need summing, you can check out these other MATLAB vector-wise functions that also have this new DIM behavior: all, any, bounds, max, min, mean, median, mode, prod, std, and var.

Let me leave you with a little bit of programming advice related to these functions. If you are certain that the input argument you are passing to one of these functions is a vector (because you constructed or computed it yourself), then you can safely use the single-input syntax, like sum(v). Otherwise, I recommend that you always provide the optional DIM argument to avoid certain ambiguities associated with MATLAB's forgiving definition of "vector."




Published with MATLAB® R2019a

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