55:148 Digital Image Processing
Chapter 5, Part III
Segmentation: Region growing segmentation
Sections from Chapter 5 according to the WWW Syllabus.
Chapter 5.3 Overview:
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
- Segmentations resulting from edge-based methods and region growing methods are not
usually exactly the same.
- Combination of results may often be a good idea.
- 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
- Regions have already been defined
- Resulting regions of the segmented image must be both homogeneous and maximal.
- 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
- 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 [s_ij = |f(x_i) - f(x_j)|].
- 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
- A good data structure to use can be a planar region adjacency graph.
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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).
- The concepts of watersheds and catchment basins are well known in
- 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.
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.
Region growing post-processing
- Region growing often results in undergrowing or overgrowing as a result of non-optimal
- A variety of post-processors has been developed.
- Some of them combine segmentation information obtained from region growing and
- 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.
Last Modified: November 6, 2003