Different representations of images and their purpose
These are some representations that I already gathered information on, so I'll list them here.


Pixel based representation


simplest to define, simple neighborhood relations between elements (4,8,6-connectivity (1))
only local information for each element
big number of elements in the representation (used for displaying the image, applications with a lot of noise/details: e.g. medical imaging)

Block-based representations


image divided in a set of (rectangular) arrays
number of elements slightly smaller than with pixel-based, still only local information
both gray-scale and binary images
uses in compression ((2), (3), (4)), segmentation ((4), (5)), extracting different image features ((5), (6), (7))

Region based (sometime also super-pixels) representations


regions not rectangular; formed by grouping similar and connected pixels, usually using over-segmentation
adjacency information between regions (usually as RAG (region-adjacency graph (8)) or combinatorial map (9))
normalized cuts (10), graph-based segmentation (e.g. by Felzenszwalb and Huttenlocher (11)), watershed-based ((12), (13))
number of elements in the representation reduced while accuracy is kept
used for object detection and segmentation, but different unions of multiple regions have to be considered

Hierarchical representations


propose most likely unions of regions of region-based representations
image representation at different scales
only regions present in the representation have to be examined, can be constricted by scale
min-/max-tree ((14), (15)), tree of shapes ((16), (17)), binary partition tree (18), $\alpha$-tree (19), ...
used for: object detection (20), video segmentation (21), image segmentation and filtering ((22), (23)), image simplification (24)