Regions

Documentation for Regions.

Regions.jl defines a set of types and functions that model a discrete 2-dimensional region concept.

Example of a region

In order to use the types and functions defined in the Regions package, you must first install it with the package manager and then make it known to your module:

julia> using Pkg
julia> using Pkg.add(path="D:/!julia/Regions")

julia> using Regions

Regions can be used for various purposes in machine vision and image processing. Since they provide an efficient run-length encoding of binary images, they avoid the need to touch every pixel when doing binary morphology and thus enable substantial speedup of such operations. Regions are also the basis for binary blob analysis, where the calculation of shape-based features is also substantially accelerated because of the run-length encoding. Finally, regions can be used as the domain of image processing functions.

Introduction

A region can be seen as a set of discrete coordinates in the cartesian plane. In fact, one of the main motivations for the region concept was to model a set of pixel locations for image processing purposes.

A region is represented with a sorted list of horizontal runs. Runs themselves are represented with a horizontal columns range and a vertical row coordinate.

Region and runs

Here is how this region can be created using the Julia REPL (assuming the origin (0, 0) is at the upper left):

julia> Region([Run(0, 1:4), Run(1, 0:5), Run(2, 1:2), Run(2, 4:6), Run(3, 1:2), Run(3, 5:5), Run(4, 1:2), Run(4, 4:5), Run(5, 2:4)])
Region(Run[Run(0, 1:4), Run(1, 0:5), Run(2, 1:2), Run(2, 4:6), Run(3, 1:2), Run(3, 5:5), Run(4, 1:2), Run(4, 4:5), Run(5, 2:4)], false)

Range

The most basic building block of a region is a range. The UnitRange{Int64} is a suitable type and can be written like this:

julia> 0:99
0:99

julia> (0:99).start
0

julia> (0:99).stop
99

julia> length(0:99)
100

julia> length(-50:50)
101

A range where the stop is less than the start is considered empty.

julia> isempty(0:0)
false

julia> isempty(1:0)
true

The natural sort order of ranges is to sort them by their start.

julia> 0:100 < 1:101
true

julia> 0:1 < 1:100
true

julia> 0:50 < 0:100
true

julia> isless(0:100, 1:101)
true

Inversion mirrors a range at the origin.

julia> invert(0:100)
-100:0

julia> invert(invert(5:10))
5:10

Translation moves a range by an offset.

julia> translate(0:100, 50)
50:150

julia> (10:20) + 30
40:50

julia> 10 + (20:30)
30:40

julia> (50:100) - 10
40:90

You can check whether a value is contained in a range.

julia> contains(10:20, 10)
true

julia> contains(10:20, 15)
true

julia> contains(10:20, 20)
true

julia> contains(10:20, 9)
false

julia> 14 ∈ 10:20
true

Two ranges can overlap or touch.

julia> isoverlapping(10:20, 5:25)
true

julia> isoverlapping(0:0, 1:1)
false

julia> istouching(0:0, 1:1)
true

julia> istouching(0:0, 2:2)
false

Run

A run combines a vertical row coordinate with a range of horizontal columns coordinates.

An empty run is a run whose columns range is empty.

julia> isempty(Run(0, 0:-1))
true

julia> isempty(Run(0, 0:100))
false

The natural sort order of runs is to sort them by their row, then by their columns range.

julia> Run(0, 0:100) < Run(1, 0:100)
true

julia> Run(0, 0:100) < Run(0, 1:101)
true

Inversion mirrors a run at the origin.

julia> invert(Run(10, 50:100))
Run(-10, -100:-50)

julia> invert(invert(Run(1, 5:10)))
Run(1, 5:10)

Translation moves a run by horizontal and vertical offsets.

julia> translate(Run(0, 0:100), 10, 20)
Run(20, 10:110)

julia> Run(0, 10:20) + [30, 40]
Run(40, 40:50)

julia> Run(0, 10:20) - [30, 40]
Run(-40, -20:-10)

Region

A region is a subset of the discrete two-dimensional space. It represents a set (in the sense of mathematical set theory) of discrete coordinates. A region may be finite or infinite. A region may not be connected and it may contain holes.

Regions are an essential concept in computer vision and are useful in many respects.

Regions are not necessarily related to images; they can exist independently and without images. In addition, the coordinate space is not confined to the bounds of an image, and regions can extend into the quadrants with negative coordinates in the two-dimensional space.

Regions

Introduction
Contents
Reference
Index

Reference

Regions.Regions — Module

Regions

Main module for Regions.jl - a set of types that model a discrete 2-dimensional region concept.

Exports

Run
Region