Editing Binary image (section)

== Operations on binary images ==
An entire class of operations{{Clarify|date=September 2024}} on binary images operates on a 3×3 window of the image. This contains nine pixels, so 2<sup>9</sup> or 512 possible values. Considering only the central pixel, it is possible to define whether it remains set or unset, based on the surrounding pixels. Examples of such operations are thinning, dilating, finding branch points and endpoints, removing isolated pixels, shifting the image a pixel in any direction, and breaking H-connections. [[Conway's Game of Life]] is also an example of a 3×3 window operation.

Another class of operations is based on the notion of filtering with a structuring element. The structuring element is binary image, usually small, which is passed over the target image, in a similar manner to a filter in gray scale image processing. Since the pixels can only have two values, the morphological operations are [[mathematical morphology|erosion]] (any unset pixels within the structuring element cause the pixel to be unset) and [[mathematical morphology|dilation]] (any set pixels within the structuring element cause the pixel to be set). Important operations are [[mathematical morphology|morphological opening]] and [[mathematical morphology|morphological closing]] which consist of erosion followed by dilation and dilation followed by erosion, respectively, using the same structuring element. Opening tends to enlarge small holes, remove small objects, and separate objects. Closing retains small objects, removes holes, and joins objects.

A very important characteristic of a binary image is the [[distance transform]]. This gives the distance of every set pixel from the nearest unset pixel. The distance transform can be efficiently calculated. It allows efficient computation of [[Voronoi diagrams]], where each pixel in an image is assigned to the nearest of a set of points. It also allows skeletonization, which differs from thinning in that skeletons allow recovery of the original image. The distance transform is also useful for determining the center of the object, and for matching in image recognition.

Another class of operations is gathering orientation-free metrics. This is often important in image recognition where the orientation of the camera needs to be removed. Orientation-free metrics of a group of connected or surrounded pixels include the [[Euler number]], the perimeter, the area, the compactness, the area of holes, the minimum radius, the maximum radius.

=== Image segmentation ===
Binary images are produced from color images by [[image segmentation|segmentation]]. Segmentation is the process of assigning each pixel in the source image to two or more classes. If there are more than two classes then the usual result is several binary images. The simplest form of segmentation is probably [[Otsu's method]] which assigns pixels to foreground or background based on grayscale intensity. Another method is the [[watershed algorithm]]. [[Edge detection]] also often creates a binary image with some pixels assigned to edge pixels, and is also a first step in further segmentation.

=== Skeletons ===
[[ thinning (morphology) | Thinning]]  or [[ topological skeleton | skeletonization]]  produces binary images which consist of pixel-wide lines. The branchpoints and endpoints can then be extracted, and the image converted to a graph. This is important in image recognition, for example in [[optical character recognition]].

=== Interpretation ===
The interpretation of the pixel's binary value is also device-dependent. Some systems interprets the bit value of 0 as black and 1 as white, while others reversed the meaning of the values. In the [[TWAIN]] standard PC interface for [[Image scanner|scanners]] and [[digital camera]]s, the first flavor is called ''[[Vanilla (computing)|vanilla]]'' and the reversed one ''chocolate''.

[[Dither]]ing is often used for displaying{{Context inline|date=September 2024}} [[halftone]] images.<ref>{{Cite book|url=https://books.google.com/books?id=tN5MAQAAIAAJ&q=Dithering+used+for+displaying+binary+images.|title=Selected Papers on Digital Halftoning|last1=Allebach|first1=Jan P.|last2=Thompson|first2=Brian J.|date=1999|publisher=SPIE Optical Engineering Press|isbn=9780819431370|language=en}}</ref>