Image Processing Essay

This essay has a total of 1828 words and 10 pages.

Image Processing

Adaptive Shape Contour Tracing Algorithm
by Emad Attalla, Ph.D.

ABSTRACT
In this paper we are going to present a new shape contour tracing algorithm called
¡§Adaptive Contour Tracing Algorithm¡¨. The algorithm can trace open and closed
discontinuous digital shapes and return an ordered set of boundary points that represent
the contour of the shape. Unlike other algorithms that return boundary points that are
part of the traced shape, our algorithm returns background points that are adjacent to the
shape¡¦s contour. Furthermore, the algorithm is not hindered by shapes that are noisy
and ill-defined as it can adapt to interruptions in the shape¡¦s contour using a pre-set
tolerance and is able to scan multiple neighbors of a given point. The algorithm has a low
complexity and no restrictions on the type or size of the traced shape. The extracted
ordered set of boundary points represents the contour of a given shape and is important
for curvature-based shape descriptors.


Categories and Subject Descriptors
I.4.6 [Image Processing and Computer Vision]: Segmentation ¡V Edge and feature detection, Pixel classification
General Terms
Algorithms.
Keywords
Image Processing; Contour Tracing; Shape Boundary Extraction.

1. INTRODUCTION
Contour tracing is an important process in boundary-based shape matching. All shapes are
represented by a pattern of pixels and the contour pixels are usually a small subset of
that pattern. Curvature-based shape matching methods rely on the contour pixels to
describe the irregularities in shapes and a reliable contour-tracing algorithm is needed
to extract the boundary of shapes. If the shape has holes then another hole search
algorithm need to be applied to extract the hole pattern and such an algorithm is not part
of this article.

We developed a sequential contour-tracing algorithm denoted the ¡§Adaptive Contour
Tracing Algorithm¡¨. The algorithm computes the surrounding contour of any shape and
adapts to all types of closed curve representations whether they are filled or partially
filled digital shapes. Any pixel, 1-pixel wide lines, and full shapes could be traced and
represented by closed curves. The algorithm also accounts for discontinuities in the shape
contour and can reach nearby pixels.

The contour trace starts from the top left point or pixel closest to the shape and
proceeds clockwise following the surrounding of the contour of the shape rather than the
contour itself. The path around the contour is traced in a look-forward sweep pattern to
find the next surrounding point that is closest to the contour. The path is then closed
when the start point is found.


2. ADAPTIVE CONTOUR TRACING
Input Data: A square tessellation, Q, of Q-width x Q-height containing cells that belong
to the shape and cells that belong to the background of the shape. A Tessellation is a
group of cells (pixels in images) that has the same shape and size.

Definitions:
1- Each cell is represented by an x-y coordinate point p = (x, y)
2- The terms ¡§cell¡¨, ¡§point¡¨ and ¡§pixel¡¨ all refer to the same definition of a cell.
3- Define 8-neighbor(cell, direction) as Moore¡¦s neighborhood which is a common concept
that defines the 8-neighboring cells of any cell as shown in

4- Define i-order neighbor of any cell i-order(cell, direction) as the set of (i*8) cells,
where i > 0, that are i-1 cells away from that cell. Moore¡¦s Neighbor corresponds to
our 1-order notation. The 2-order neighbor contains 16 cells and 3-order neighbor contains
24 cells as shown in Figure 2.

5- Define 4 orientations to read cells around any cell p: (LR-Direction, RL-Direction,
DU-Direction and UD-Direction) as shown in Figure 3.

6- The top-left cell of Q has (x, y)= (1,1) and the x-axis increases from left to right
and the y-axis increases from top to bottom.

7- Let s denotes any shape cell, p denotes any background cell, c and d denote any cell, C
and D are the set of cells of i-order around cells c and d respectively.

8- When disregarding 1-pixel shapes, Define a stranded point s as a cell where all 8-neighbor or 1-order cells = p.
9- Define neighborhood tolerance factor T as the maximum i-order where the trace algorithm
should keep looking for a contour boundary.

Output Data: An ordered sequence P (p1, p2, ¡K, pn) of n contour boundary points.
The Algorithm:
- Set P to be empty.
- From top to bottom and left to right scan the cells of Q until the leftmost shape pixel
s1 with (x1, y1) coordinate is found as shown in figure 4.

- Insert p1=(x1-1,y1), left background cell next to s1, in P.
- Set startpoint = p1, previouspoint = p1, currentdirection = DU, i-order = 1
- Set p2 = getNextPoint (1, p1 , DU) and Insert p2 in P.
- Set n = 3
- While true do
(Comment: Scan all i-orders up to maximum tolerance T)
For i = 1 to T
Set pn = getNext (i, pn-1 , pn-2)
If pn = p1 then exit while loop
If pn is not empty Then
Insert pn in P
Set n = n 1
Exit For Loop
End If
Next i
End While
Function getNext
Input Parameters: i-order i, currentpoint, previouspoint
Output Parameters: nextpoint
Begin
(Comment: the direction of movement is switched between the four directions depending on
the increase and decrease in the x and y coordinate values of the previous and current
points)

If currentpoint.x > previouspoint.x Then
nextpoint = getNextPoint (i, currentpoint, LR-direction)
Else If currentpoint.x previouspoint.y Then
Continues for 5 more pages >>