International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B3. Istanbul 2004
of example shapes. In order to solve the pairwise
correspondence problem they use a polygon-based
correspondence algorithm which locates a pair of matching
sparse polygonal approximations, one for each of boundaries,
by minimising a cost function using a greedy algorithm. While
the algorithm works well with different classes of objects, it
assumes that the objects are represented by closed boundaries.
Furthermore, the algorithm was not tested on objects with
multiple closed boundaries, e.g., faces. Recently Davies er. al.
(2002) have described a method for automatically building
statistical shape models by using the Minimum Description
Length (MDL) principle. The MDL is obtained from
information theoretic considerations and the model order is
defined as the model that minimises the description length, e.g.
the model that encodes the vector observations in the most
efficient way (Walter, 2002). In their method each shape is
mapped onto a corresponding sphere where a given number of
landmarks is first selected. The positions of the landmarks are
then altered by parameterisation functions before selecting the
parameterisations that build the best model. The best model is
defined as the one, which minimises the description length of
the training set, and its quality is regulated by an objective
function that evaluates the quality of the PDM. This is a very
promising method for measuring the model quality of a
statistical shape model and results show better PDMs via
manual landmarking. However, due to the very large number
of function evaluations this optimisation method is
computationally expensive.
3. OUTLINE OF THE METHOD
In our system we used 20 close related grey images of human
hands recorded using a digital camera at a resolution
1024x768. Four people contributed with five images each of
their right hand. In our experiments three main stages have
been conducted:
l. Image segmentation or outline extraction using
thresholding and the Canny Edge Detector to obtain the
foreground (shape of the hand).
2. Freeman chain code 8-connectivity boundary
descriptor to obtain automatically the coordinate of the
boundary pixels and the direction of the boundary.
Minimum Perimeter Polygon (MPP) is used to identify
curvature descriptions.
3. Point Distribution Model (PDM) to describe the hand
shapes and their variations based on the position of the
automatic landmark points.
3.1 Extracting the hand shape
We are interested in extracting the outline of the hand shape.
The method to separate the shapes from the background was to
select a threshold
Te T[x y FG. )] (1)
where f(x,y) is the grey level of point (x,y). The threshold
image g(x,y) is defined as:
Ah
es CT
where 1 and 0 corresponds to the distinction between the
background and the foreground. For edge detection we used
750
the Canny Edge detector which find edges by looking for local
maxima of the gradient of f(x,y).
The gradient gx» z[G +G;] and edge direction
a(x, y) - tan (Gy/Gx)are computed at each point. A
vector T=[T1 T2] containing two threshold is used to find the
strong and the weak edge pixel and an edge linking is
performed by including the weak pixels to the strong. By using
those two detectors we managed to extract the shape of the
hand regardless of the grey level difference between the
foreground and the background.
3.2 Obtaining the Boundary coordinates of the shapes
For contour-based shape representation and description we
chose an 8-connectivity derivative Freeman chain code, which
is based on the fact that an arbitrary curve is represented by a
sequence of small unit length vectors and a predefined set of
possible directions. During the encoding successive contour
points are adjacent to each other. The chain code was used as a
numbered sequence that represents relative directions of
boundary elements measured in a counter-clockwise 45?
direction changes. The representation is based on 8-
connectivity and the direction of each component is coded by
the numbering scheme seen in Figure 1.
Figure l. Chain code in 8-connectivity.
The chain code was used to derive the boundary length of the
hand shapes and their direction. The entire vertical and
horizontal steps have unit length while the length of the
diagonal steps is X2 . We calculated the contour length of the
chain code as the number of vertical and horizontal components
plus J2 times the number of diagonal components. The
diameter of the shape boundary b is defined as:
D(b)=max[D(p;,p)] (3)
HJ
where D is the Euclidean distance measure between D;
and p, and is defines as:
D(ipjNGi-x *xj-vj? — (4)
where (X Jp XJ) coordinates ofthe p; and p; points.
One constrain of the chain codes is that in order to work
properly the boundary should be a closed boundary, and a
starting point should be defined. In order to choose an initial
starting point on the closed boundary, which will have the
associated parameter value, u=1 we searched where the vertical
and the horizontal principal axes, the axes that pass though the
centroid of the boundary points, intersect. The horizontal
extension of the intersection meets the thumb, which was
selected as the starting point of the chain code. It is assumed
that this point is fixed for all shapes. This is reasonable since
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