Question

I want to tackle some image-processing problems in Haskell. I’m working with both bitonal (bitmap) and color images with millions of pixels. I have a number of questions:

1. On what basis should I choose between Vector.Unboxed and UArray? They are both unboxed arrays, but the Vector abstraction seems heavily advertised, particular around loop fusion. Is Vector always better? If not, when should I use which representation?

2. For color images I will wish to store triples of 16-bit integers or triples of single-precision floating-point numbers. For this purpose, is either Vector or UArray easier to use? More performant?

3. For bitonal images I will need to store only 1 bit per pixel. Is there a predefined datatype that can help me here by packing multiple pixels into a word, or am I on my own?

4. Finally, my arrays are two-dimensional. I suppose I could deal with the extra indirection imposed by a representation as “array of arrays” (or vector of vectors), but I’d prefer an abstraction that has index-mapping support. Can anyone recommend anything from a standard library or from Hackage?

I am a functional programmer and have no need for mutation 🙂

Answer 1

For multi-dimensional arrays, the current best option in Haskell, in my view, is repa.

Repa provides high performance, regular, multi-dimensional, shape polymorphic parallel arrays. All numeric data is stored unboxed. Functions written with the Repa combinators are automatically parallel provided you supply +RTS -Nwhatever on the command line when running the program.

Recently, it has been used for some image processing problems:

• Real time edge detection
• Efficient Parallel Stencil Convolution in Haskell

I’ve started writing a tutorial on the use of repa, which is a good place to start if you already know Haskell arrays, or the vector library. The key stepping stone is the use of shape types instead of simple index types, to address multidimensional indices (and even stencils).

The repa-io package includes support for reading and writing .bmp image files, though support for more formats is needed.

Addressing your specific questions, here is a graphic, with discussion:

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On what basis should I choose between Vector.Unboxed and UArray?

They have approximately the same underlying representation, however, the primary difference is the breadth of the API for working with vectors: they have almost all the operations you’d normally associate with lists (with a fusion-driven optimization framework), while UArray have almost no API.

For color images I will wish to store triples of 16-bit integers or triples of single-precision floating-point numbers.

UArray has better support for multi-dimensional data, as it can use arbitrary data types for indexing. While this is possible in Vector (by writing an instance of UA for your element type), it isn’t the primary goal of Vector — instead, this is where Repa steps in, making it very easy to use custom data types stored in an efficient manner, thanks to the shape indexing.

In Repa, your triple of shorts would have the type:

Array DIM3 Word16

That is, a 3D array of Word16s.

For bitonal images I will need to store only 1 bit per pixel.

UArrays pack Bools as bits, Vector uses the instance for Bool which does do bit packing, instead using a representation based on Word8. Howver, it is easy to write a bit-packing implementation for vectors — here is one, from the (obsolete) uvector library. Under the hood, Repa uses Vectors, so I think it inherits that libraries representation choices.

Is there a predefined datatype that can help me here by packing multiple pixels into a word

You can use the existing instances for any of the libraries, for different word types, but you may need to write a few helpers using Data.Bits to roll and unroll packed data.

Finally, my arrays are two-dimensional

UArray and Repa support efficient multi-dimensional arrays. Repa also has a rich interface for doing so. Vector on its own does not.

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Notable mentions:

• hmatrix, a custom array type with extensive bindings to linear algebra packages. Should be bound to use the vector or repa types.
• ix-shapeable, getting more flexible indexing from regular arrays
• chalkboard, Andy Gill’s library for manipulating 2D images
• codec-image-devil, read and write various image formats to UArray