Chapter 5.3

Chapter 5.3 Region growing segmentation

Overview:

Region merging
Region splitting
Splitting and merging
Watersheds

Region growing segmentation

	Edge-based segmentation: borders between regions
	Region-based segmentation: direct construction of regions

It is easy to construct regions from their borders and it is easy to detect borders of existing regions.

Segmentations resulting from edge-based methods and region growing methods are not usually exactly the same.

Region growing techniques are generally better in noisy images where edges are extremely difficult to detect.

Homogeneity of regions is used as the main segmentation criterion in region growing.

The criteria for homogeneity:

	gray level
	color, texture
	shape
	model
	etc.

Regions have already been defined

Further assumptions:

Resulting regions of the segmented image must be both homogeneous and maximal.

Region merging

Specific methods differ in the definition of the starting segmentation and in the criterion for merging. The result of region merging usually depends on the order in which regions are merged.

	The simplest methods begin merging by starting the segmentation using regions of 2x2, 4x4 or 8x8 pixels. Region descriptions are then based on their statistical gray level properties.
	A region description is compared with the description of an adjacent region; if they match, they are merged into a larger region and a new region description is computed. Otherwise regions are marked as non-matching.
	Merging of adjacent regions continues between all neighbors, including newly formed ones. If a region cannot be merged with any of its neighbors, it is marked `final' and the merging process stops when all image regions are so marked.

The data structure called supergrid carries all the necessary information for region merging in 4-adjacency using crack edges.

Merging heuristics:

	Two adjacent regions are merged if a significant part of their common boundary consists of weak edges
	Two adjacent regions are also merged if a significant part of their common boundary consists of weak edges, but in this case not considering the total length of the region borders.

Of the two given heuristics, the first is more general and the second cannot be used alone because it does not consider the influence of different region sizes.

Edge significance can be evaluated according to the formula

where v_ij=1 indicates a significant edge, v_ij=0 a weak edge, T_1 is a preset threshold, and s_ij is the crack edge value.

	The supergrid data structure allows precise work with edges and borders but a big disadvantage of this data structure is that it is not suitable for the representation of regions.
	A good data structure to use can be a planar region adjacency graph.

Region splitting

Region splitting is the opposite of region merging.

	It begins with the whole image represented as a single region which does not usually satisfy the condition of homogeneity.
	The existing image regions are sequentially split to satisfy all the above given conditions of homogeneity.

Region splitting does not result in the same segmentation even if the same homogeneity criteria are used.

Region splitting methods generally use similar criteria of homogeneity as region merging methods, and only differ in the direction of their application.

Splitting and merging

	A combination of splitting and merging may result in a method with the advantages of both approaches.
	Split-and-merge approaches work using pyramid image representations; regions are square-shaped and correspond to elements of the appropriate pyramid level.

	If any region in any pyramid level is not homogeneous (excluding the lowest level), it is split into four subregions -- these are elements of higher resolution at the level below.
	If four regions exist at any pyramid level with approximately the same value of homogeneity measure, they are merged into a single region in an upper pyramid level.

The segmentation process can be understood as the construction of a segmentation quadtree where each leaf node represents a homogeneous region.

Splitting and merging corresponds to removing or building parts of the segmentation quadtree.

Split-and-merge methods usually store the adjacency information in region adjacency graphs (or similar data structures).

Using segmentation trees, in which regions do not have to be contiguous, is both implementationally and computationally easier.

An unpleasant drawback of segmentation quadtrees is the square region shape assumption

merging of regions which are not part of the same branch of the segmentation tree

Because both split-and-merge processing options are available, the starting segmentation does not have to satisfy any of the homogeneity conditions.

A pyramid data structure with overlapping regions is an interesting modification of this method.

Each region has four potential parent elements in the upper pyramid level and sixteen possible child elements in the lower pyramid level.

Segmentation tree generation begins in the lowest pyramid level. Properties of each region are compared with properties of each of its potential parents and the segmentation branch is linked to the most similar of them.

After construction of the tree is complete, all the homogeneity values of all the elements in the pyramid data structure are recomputed to be based on child-region properties only.

This recomputed pyramid data structure is used to generate a new segmentation tree, beginning again at the lowest level.

The pyramid updating process and new segmentation tree generation is repeated until no significant segmentation changes can be detected between steps.

The highest level of the segmentation tree must correspond to the expected number of image regions and the pyramid height defines the maximum number of segmentation branches.

If the number of regions in an image is less than 2^n, some regions can be represented by more than one element in the highest pyramid level.

	Considerably lower memory requirements can be found in a single-pass split-and-merge segmentation.
	A local splitting pattern is detected in each 2x2 pixel image block and regions are merged in overlapping blocks of the same size.

	The image blocks overlap during the image search.
	Except for locations at the image borders, three of the four pixels have been assigned a label in previous search locations, but these labels do not necessarily match the splitting pattern found in the processed block.
	If a mismatch is detected in step 3 of the algorithm, it is necessary to resolve possibilities of merging regions that were considered separate so far - to assign the same label to two regions previously labeled differently.

Two regions R_1 and R_2 are merged into a region R_3 if

where m_1 and m_2 are the mean gray level values in regions R_1 and R_2, and T is some appropriate threshold.

	If region merging is not allowed, regions keep their previous labels.
	If larger blocks are used, more complex image properties can be included in the homogeneity criteria (even if these larger blocks are divided into 2x2 sub-blocks to determine the splitting pattern).

Watershed Segmentation

	The concepts of watersheds and catchment basins are well known in topography.
	Watershed lines divide individual catchment basins.
	The North American Continental Divide is a textbook example of a watershed line with catchment basins formed by the Atlantic and Pacific Oceans.

	Image data may be interpreted as a topographic surface where the gradient image gray-levels represent altitudes.
	Region edges correspond to high watersheds and low-gradient region interiors correspond to catchment basins.
	Catchment basins of the topographic surface are homogeneous in the sense that all pixels belonging to the same catchment basin are connected with the basin's region of minimum altitude (gray-level) by a simple path of pixels that have monotonically decreasing altitude (gray-level) along the path.
	Such catchment basins then represent the regions of the segmented image.

Concept of watersheds and catchment basins is quite straightforward.

Early watershed methods resulted in either slow or inaccurate execution.

Most of the existing algorithms start with extraction of potential watershed line pixels using a local 3 x 3 operation, which are then connected into geomorphological networks in subsequent steps. Due to the local character of the first step, these approaches are often inaccurate.

A watershed transformation was also introduced in the context of mathematical morphology - computationally demanding and therefore time consuming.

Two basic approaches to watershed image segmentation.

	The first one starts with finding a downstream path from each pixel of the image to a local minimum of image surface altitude.
	A catchment basin is then defined as the set of pixels for which their respective downstream paths all end up in the same altitude minimum.
	While the downstream paths are easy to determine for continuous altitude surfaces by calculating the local gradients, no rules exist to define the downstream paths uniquely for digital surfaces.
	The second approach is essentially dual to the first one; instead of identifying the downstream paths, the catchment basins fill from the bottom.
	Imagine that there is a hole in each local minimum, and that the topographic surface is immersed in water - water starts filling all catchment basins, minima of which are under the water level. If two catchment basins would merge as a result of further immersion, a dam is built all the way to the highest surface altitude and the dam represents the watershed line.
	An efficient algorithm is based on sorting the pixels in increasing order of their gray values, followed by a flooding step consisting of a fast breadth-first scanning of all pixels in the order of their gray-levels.
	During the sorting step, a brightness histogram is computed. Simultaneously, a list of pointers to pixels of gray-level h is created and associated with each histogram gray-level to enable direct access to all pixels of any gray-level.
	Information about the image pixel sorting is used extensively in the flooding step.
	Suppose the flooding has been completed up to a level (gray-level, altitude) k. Then every pixel having gray-level less than or equal to k has already been assigned a unique catchment basin label.
	Next, pixels having gray-level k+1 must be processed; all such pixels can be found in the list that was prepared in the sorting step - consequently, all these pixels can be accessed directly.
	A pixel having gray-level k+1 may belong to a catchment basin labeled l ("el") if at least one of its neighbors already carries this label.
	Pixels that represent potential catchment basin members are put in a first-in first-out queue and await further processing.
	Geodesic influence zones are computed for all hitherto determined catchment basins.
	A geodesic influence zone of a catchment basin l_i is the locus of non-labeled image pixels of gray-level k+1 that are contiguous with the catchment basin l_i (contiguous within the region of pixels of gray-level k+1) for which their distance to l_i is smaller than their distance to any other catchment basin l_j.

	All pixels with gray-level k+1 that belong to the influence zone of a catchment basin labeled l are also labeled with the label l, thus causing the catchment basin to grow.
	The pixels from the queue are processed sequentially, and all pixels from the queue that cannot be assigned an existing label represent newly discovered catchment basins and are marked with new and unique labels.
	Example of watershed segmentation.

	Raw watershed segmentation produces a severely oversegmented image with hundreds or thousands of catchment basins.
	To overcome this problem, region markers and other approaches have been suggested to generate good segmentation.

While this method would work well in the continuous space with the watershed lines accurately dividing the adjacent catchment basins, the watersheds in images with large plateaus may be quite thick in discrete spaces:

Region growing post-processing

Region growing often results in undergrowing or overgrowing as a result of non-optimal parameter setting.

Some of them combine segmentation information obtained from region growing and edge-based segmentation.

Simpler post-processors are based on general heuristics and decrease the number of small regions in the segmented image that cannot be merged with any adjacent region according to the originally applied homogeneity criteria.

This algorithm will execute much faster if all regions smaller than a preselected size are merged with their neighbors without having to order them by size.

Chapter 5.3

Page last updated: 04/02/01