1. A Graph based Geometric Approach to Contour Extraction from Noisy Binary Images
Amal Dev Parakkat, Jiju Peethambaran, Philumon Joseph and Ramanathan Muthuganapathy
Computer-Aided Design and Applications, 11, 2014
Presented by: Yang Yu
Jan. 24, 2015

2. Motivation
The boundary lines of geometric objects in an image is a contour.
The computation time will be reduced if the feature extraction are applied on the contour.
Gaussian filter reduces the noise, but weakens the contrast across the edges and blend adjacent edges.
High compression ratio and smooth representation compared to pixel based methods.

3. Overview
This paper proposes a geometrybased contour extraction approach that works well with noisy binary images.
Color segmentation distinguishes the object pixels from the background pixels.
All object pattern pixels are extracted as a point set.
A geometric graph is constructed on these extracted points,
All border points are connected by using the clockwise turn angle at each border point.
The extracted contour is simplified using collinearity check.

4. Point Extraction
A color segmentation extract the object pattern from the image.
The foreground pixels are transformed into a set of points.
(a) Sampled part of Input image with object pattern in white color
(b) Corresponding points

5. Geometric Graph Construction
If less than the threshold 1.415, connect two points
(a) using parameter value l , (b) linking a point from edge.
Left: Input point set,
Middle: Corresponding geometric graph with appropriate value of l,
Right: Contour extracted by this algorithm.

6. Point Linking
v1: least x value, number of edges greater than 1. then least y value. Origin point lies at the top left.
v2: x2 ≥ x1 and y2>y1.
vq: largest clockwise turn angle as the next candidate point

7. Noise Point Positions
Case 3 and 4 add (remove) an object point from contour, others have no impact on contour.
As the object size increases, the visual impact of false positives and true negatives on the extracted contour becomes more negligible.
Possible positions for the occurrence of noise

8. Contour Simplification
Reduce the space needed to store the contour.
Simplification is based on the fact of the high probability for the existence of collinear points.
Left: A sample contour,
Middle: Points selected after contour simplification,
Right: Simplified contour.

9. Contour Simplification
pi is considered as an irregularity when the area of Δpipjpk is less than parameter ‘ ’.
small irregularities is noise. p denotes number of pixels needed to represent the contour.

10. Comparison Results (a) Original image, (b) Binary image,
(c) Contour extracted by this algorithm,
(d) Output of Sobel edge detector,
(e) Output of Canny edge detector.

11. Qualitative Results
When dealing with color or grey-scale images, the image has to be converted to binary.
Input image, Binary image, Image with Gaussian noise, Output of this algorithm

12. Robustness to Noise
First binarized, then injected with Gaussian noises.
The noise makes a sharp transition in black background which will be misinterpreted as an edge
Original image, Gaussian noise image, Sobel edge detector, Canny edge detector, Result of this algorithm.

13. Gaussian Noise Effect
This algorithm rely on proximity and orientation of points, so the results are noise free.
Gaussian noise intensity values is either 0 or 255.
No edge between any noisy points or between noisy and object points, because the distance greater than
Once the Gaussian noise goes above 70%, edges between noisy points are created and this will affect the subsequent contour extraction.
Image with noise, Extracted point set, Geometric graph constructed

14. Compression
The number of pixels extracted as the contour are relatively low. The number of pixels reduced to 2.4% %

15. Conclusions The extracted contour is more compact and smooth.
The compression ratio for noisy images is very high.
Suitable for Input binary images having background noise (MRI scans or satellite images).
Work with binary images with single object embedded in it.
Future work
Contour extraction from grey and color images with multiple objects.
Extraction of open contours and hole boundaries from images.
Development of an automated medical diagnosis system using contour matching.
Use in unsupervised inspection of machine parts for geometric irregularity.