by Emad Attalla, Ph.D.
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
Image Processing; Contour Tracing; Shape Boundary Extraction.
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...