Manifolds are mathematical spaces whose points have Euclidean neighborhoods, but whose global structure could be
more complex. A one dimensional manifold has a neighborhood that resembles a line. A two dimensional one resembles
a plane. If we consider a one dimensional example, most system neighborhoods cannot be represented optimally by a
straight line. A multi-ordered nonlinear line would be better suited to represent most data. A learning algorithm to model
the pipeline, based on Fischer Linear Discriminant (FLD), using least squares estimation is presented in this paper. Face
patterns are known to show continuous variability. Yet face images of one individual tend to cluster together and can be
considered as a neighborhood. Such similar patterns form a pipeline in state space that can be used for pattern
classification. Multiple patterns can be trained by having separate lines for each pattern. Face points are now projected
onto a low-dimensional mean nonlinear pipe-line, thus providing an easy intuitive way to place new points. Given a test
point/face, the classification problem is now simplified to checking the nearest neighbors. This can be done by finding
the minimum distance pipe-line from the test-point. The proposed representation of a face image results in improved
accuracy when compared to the classical point representation.
A modular approach on an adaptive thresholding method for segmentation of cell regions in bioelectric images with
complex lighting environments and background conditions is presented in this paper. Preprocessing steps involve lowpass
filtering of the image and local contrast enhancement. This image is then adaptively thresholded which produces a
binary image. The binary image consists of cell regions and the edges of a metal electrode that show up as bright spots.
A local region based approach is used to distinguish between cell regions and the metal electrode tip that cause bright
spots. Regional properties such as area are used to separate the cell regions from the non-cell regions. Special emphasis
is given on the detection of twins and triplet cells with the help of watershed transformation, which might have been lost
if form-factor alone were to be used as the geometrical descriptor to separate the cell and the non-cell regions.