analysis of shape biomedical image processing course, yevhen hlushchuk and jukka parviainen
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Analysis of shape
Biomedical Image processing course,
Yevhen Hlushchuk
and Jukka Parviainen
Contents
• Representation of shapes and contours– signatures– chain coding– segmentation of the contours– polygonal and parabolic modeling– thinning and skeletonization
• Shape factors– compactness– moments– chord-length statistics
Shape importance in medicine
• most human organs possess certain reedily identifiable shapes (deviations might be caused by a pathology)
• very important issue is differentiation between malignant and benign tumours, general rule: benign masses have smooth boundaries and simplper shapes (not so many angles :)
Signatures of contours
• The most general representation of the contouris in terms (x,y) coordinates.
• Converting coordinate-based to distances from each contour point to reference point (centroid). Radial distance may also be used but has drawbacks for irregular shapes. FIG 6.2, 6.3 here (benign masses – smooth signatures)
Chain coding
• relies on specifying the starting point, direction of traversal (clockwise ot counter-clockwise) and movement need to be done to get to the next point (e.g., 1 pixel up, or 1 pixel right). Number of different movements used in the code defines how fine is the representation (compare 4 and 8) Figure 6.5 here
Chain code
Chain code
• Advantages:– more compact representation (2-3 bits per
point)– invariant to shift or translation– certain possibilities to scaling and rotattion (by
45 or 90 degrees)– nice to calculate the length of the contour,
area of a closed loop, check for multiple loops and closure
Segmentation of the contour
• Useful step before analysis and modeling
• Book author’s own example :– locating points of inflections
(f’’=0; f’=!0; f’’’=!0)– irrelevant points of
inflection (on straight segments) – cumulative sums might help
Inflection points
Polygonal modeling
• prespicifying the number of segments (e.g., using points of inflections)
• main criteria – arch-to-chord deviation:– if it exceeds certain threshold the curved part
is segmented at the point of the max deviation
Parabolic modeling
• straight segments may not contribute much to the discrimination between benign and malignant masses
• After all, classification accuracy was 76% (compared to what? radiologist? or histology? )with a set of 54 contours
Thinning and skeletonization
Shape factors
• Idea is to encode the nature or form of a conotur using a small number of features, called shape factors
• Basic properties:– invariance to spatial shift– invariance to rotation– invariance to scaling
Shape factors
• Compactness is a popular measure of the efficiency of the contour to contain a given area and defined as perimeter in the second power divided by the area contained within the contour (circle is the best here :).
• Moments of the contours: to the centre of the image , to the centroid of the contour, normalized and so on. High order momens are sensitive to noise (thus different types of normalization on low-order moments have been attempted)
Chord-length statistics
• One can calculate the mean, deviation, skewness and curtosis for the cord-lengths (Kolgorov-Smirnov statistics).
• Nice about it: – invariant to spatial shift– invariant to rotation– invariant to scaling
• Not so nice – ”certain invariance to shape ” (objects with different shapes might still have similar statistics)
Summary (contents)
• Representation of shapes and contours– signatures– chain coding– segmentation of the contours– polygonal and parabolic modeling– thinning and skeletonization
• Shape factors– compactness– moments– chord-length statistics
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