Image transformation and processing

Image detectors can be viewed as a mysterious "black box" that in a certain way transforms (transforms) the input image of the scene (image function) f(x,y) into the output image g(x,y). The result of the transformation is determined by the properties of the "black box" and is described by the so-called transformation function h(x,y). With a suitable shape of the transformation function, the required image modification can be achieved: e.g. brightness and contrast adjustment, color scale change, pseudo-coloring, smoothing (noise removal), sharpening, edge detection, morphological operations, conversion to the frequency domain, image reconstruction from projections, etc.).

Point operations
Point operations are used to transform an image point by point, where each point of the output image is affected by only one point of the input image. The required dependency is usually realized by a LUT (Look Up Table) modification table, which carries information about the transformation of each given point. Point operations are used when adjusting color (color scale, pseudo-coloring), dynamic range, brightness, or contrast, but can also be applied when enhancing or segmenting an image (e.g., thresholding).

Local operations
For local operations, each point of the output image is affected only by the surrounding points of the input image covered by a suitable convolution mask. The data is transformed in such a way that certain structures are highlighted or suppressed in the image – a process often referred to as filtering. Filtering is mainly used for image smoothing, noise suppression, image sharpening, preparation for segmentation (e.g. edge detection) or for morphological operations with the image, image reconstruction or detection and classification of objects in the image. Masks can be of different shapes and sizes. Square masks ranging in size from 3x3 to about 9x9 are usually used.

Global operations
Used to edit the image as a whole. Each point of the output image is affected by all points of the input image for global operations. This mainly includes restoration mechanisms (removal of image distortion, image reconstruction from projections, depth dimension reconstruction, noise suppression, etc.) or two-dimensional image transformations (e.g. Fourier transformation, cosine transformation, etc.). Global adjustments can also be used when compressing image data, for texture analysis, or for object recognition.