Image Segmentation
• Image segmentation (segmentace obrazu)
– division or separation of the image into segments (connected regions)
of similar properties (attributes).
• Haralick and Shapiro
– ”The regions should be uniform and homogenous with respect to some
characteristic such as intensity value or texture. Region interiors
should be simple and without many small holes. Adjacent regions
should have significantly different values with respect to the
characteristic on which they are uniform. Boundaries of each segment
should be simple, not ragged, and must be spatially accurate.”
Approaches to Image Segmentation
• Thresholding
– Global thresholding
– Local (adaptive) thresholding
• Edge detection
– Curve fitting
– Heuristic edge linking
– Hough transform
• Region-based methods
– Region growing
– Region splitting
– Split and merge
• Texture segmentation
– Amplitude approach
– Edge-based approach
• Clustering methods
– Cluster analysis
• Template matching
– Correlation with pattern
• Advanced methods
– Mathematical morphology tools
– Watershed algorithm
– LCS algorithm
Thresholding
• Thresholding (prahování)
– the pixels are split into regions based on their intensity: the pixels with
the intensity higher than a predefined threshold value belong to a
different region than the pixels with intensity lower than the threshold
• Global thresholding = thresholding
– the threshold is equal for all pixels in the image
(independent of their position in the image)
• Local (adaptive) thresholding
– the threshold depends on the position of the pixel in the image
• Determination of the threshold
– Manual: the threshold is set by user using a slider with preview
– Automatic: using intensity histogram analysis
Bilevel Thresholding
• Bilevel thresholding (dvouúrovňové prahování)
– Idea: If the image is simple (objects of similar intensity on a uniform
background, e.g. typed text or cells of the same type), the histogram
contains two peaks with a valley between them. The threshold is taken
at the valley (at the local minimum between the two maxima).
– For more precise determination of the minimum, the valley can be
fitted by parabola.
– If the histogram does not contain two peaks, sometimes it helps to
compute the histogram only of those pixels, where the magnitude of
Laplacian is large.
Multilevel Thresholding
• Multilevel thresholding (víceúrovňové prahování)
– Idea: If the image contains several types of objects on a uniform
background and each type of object has got a specific intensity range,
(e.g. a mixture of cells of several types), the histogram contains
several peaks with valleys between them. Several thresholds are taken,
one threshold per each valley (at the local minimum between the two
neighboring maxima).
– For more precise determination of the minimum, the valley can be
fitted by parabola.
Thresholding of Color Images
• Color images can be segmented in the following ways:
– The thresholding is performed in each color channel (RGB) separately.
– The thresholding is performed not according to the intensity but
according to hue, saturation or other characteristics.
– The user (or computer) selects specific ranges of colors for each object
type.
Local (Adaptive) Thresholding
• Motivation
a) Uneven background intensity
b) Uniform background intensity but uneven object intensities which
do not form individual peaks in the histogram (the peaks of individual object types overlap in the histogram forming one wider peak)
Local (Adaptive) Thresholding
• Solutions
1) The image is divided into regular subregions (e.g. squares) and the
threshold is set individually for each region using the analysis of the
histogram computed from this particular region.
• Not very good results at the edges between regions.
2) The same as 1) but thresholds for individual pixels are determined
using interpolation of the threshold value among the regions.
• Good in case a) but not in case b).
3) First, global thresholding is performed to separate background from
objects. Then, for each object, local intensity histogram is computed
and threshold determined. All objects are re-segmented with individual
thresholds
• Good in case b) but problems arise when two types of objects (of different
intensities) touch each other and are treated as one region after the initial
global thresholding.
Local Thresholding Example
Original grayscale image
Low global threshold
High global threshold
Individual threshold for each object
Edge Detection
• Segmentation based on edge detection
– Determination of object boundaries from a gradient image
(1st derivative of the original image) or Laplacian image
(2nd derivative of the original image), which are usually
obtained using Sobel or Laplacian filters, respectively.
• Problem
– Boundaries in gradient image are not continuous!
• Solution 1: Curve fitting
– Assumption: Objects in the image are simple, the edge map
does not contain branches.
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•
•
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Iterative end-point line fitting
Other polygon fittings
Polynomial fittings
Bezier polynomial or spline fittings
Edge Detection
• Solution 2: Heuristic edge linking
– Assumption: objects in the image are not too complicated.
– Boundary points are linked with lines using a certain heuristic
algorithm, then multiple connections and branches are deleted and
finally boundary fragments are connected with ”bridges”.
• Solution 3: Hough transform
– Assumption: objects in the image are not too complicated.
– Hough transform is a transformation of a line in Cartesian coordinates
to a point in polar coordinates according to the equation:
r  x cosq  y sinq
where r is the normal distance of the line from the origin and q is the
angle of the normal with respect to the x axis.
Hough Transform
• Basic facts about Hough transform
– A line is transformed to a point.
– A family of lines passing through a common point is transformed to
a connected set of points (a curve).
– Three families of lines passing through 3 colinear points are
transformed to 3 curves that intersect at a single point corresponding
to a line in Cartesian coordinates passing through these three points.
– In discrete Hough transform of a binary image, each non-zero data
point in the original image is transformed to a curve in the polar
domain, which is quantized into cells (pixels). If the curve passes the
given cell in polar coordinates, the cell is incremented by one count.
– In discrete Hough transform of a gray-scale image, the cell is
incremented by a value corresponding to the gradient magnitude
(i.e. strong edges have bigger influence than weak edges).
Hough Transform
• Hough transform edge linking
– Each cell in the Hough image whose magnitude is sufficiently large
defines a straight line that passes through the original image.
– If this line is overlaid with the image edge map (gradient image),
it should cover the missing links of straight line edge segments.
– The missing links must be filled using a certain heuristic method
(like in Solution 2).
• Generalized Hough transform
– Hough transform can be generalized for arbitrary functions (arbitrary
shapes). Besides lines, the most important is the detection of circles in
images. In this case, the parameters in Hough space are the circle
center (x,y) and radius (r) if it is not known a priori.
• Recommended web pages on Hough transform
http://cs-alb-pc3.massey.ac.nz/notes/59318/l11.html
http://markschulze.net/java/hough/