Steve on Image Processing and MATLAB

Concepts, algorithms & MATLAB

Changes to SUM and DIM 3

Posted by Steve Eddins,

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."


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Published with MATLAB® R2019a

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