Transactions on Mass-Data Analysis of Images and Signals with Applications in Medicine, Biotechnology, Chemistry and Food Industry

The present issue of the International Journal Transactions on Mass-Data Analysis of
Images and Signals proposes two papers regarding the alignment of shapes from a
point correspondence perspective. The first paper [1] is dedicated to the computation
of the similarity between shapes that can differ a lot from each other whilst the second
paper [2] presents a shape-based matching algorithm that takes into account the variability
of both the shapes used to build the base of cases and the shapes of the unseen
objects.
In more detail, the first paper [1] addresses the problem of aligning shapes that can
be very different such as a concave shape and a convex one. To this end, each shape is
considered as a point set and point correspondences between each point set are established.
Once the latter are achieved, the similarity between the shapes is computed.
With regard to point correspondence, an essential requirement is symmetry: the same
mapping should be obtained when matching shape A to shape B or shape B to shape
A. A one-to-one point correspondence usually comes along with such a requirement.
Knowing that the cardinality of each point set might differ from each other, some
points, namely outliers, might not be mapped. When it comes to aligning very different
shapes, existing algorithms produce illegal correspondences, i. e. correspondences
that, when following the boundaries, do not guarantee an increase in the lengths of the
arc paths defined with respect to the first point correspondence that is considered.
Such illegal correspondences can lead to similarity measures that underestimate the
difference between two shapes. The authors thus propose an original algorithm for
aligning 2D-shapes by computing one-to-one legal and symmetric point correspondences.
This algorithm takes as inputs two shapes that are normalized using a scale
factor and centered at the origin. The shape with the highest number of points is
aligned to the other one by considering all possible rotations. Each alignment is based
on ordered sets of points to enforce point correspondence legality. The similarity
measure is computed for each rotation and the best one is retained. This measure is
based on the Euclidean distances between corresponding points, takes into account
outliers, handles wavy shapes and is normalized to run between 0 and 1. Experiments
on both synthetic (geometric shapes) and real data (spores of six fungal strains)
demonstrate the potential of the approach.
The second paper [2] proposes a shape-based algorithm that matches unseen objects
to the cases of a base. Such a base is necessary to detect objects with high variance.
It is built from examples which are grouped using a clustering technique providing,
for each cluster, a generalized shape than can be either a mean shape or the shape
which is the most representative one. For each generalized shape, which is a point set,
the maximum Euclidean distance between its points and the points of the other shapes
of the cluster is selected as the maximum permissible distance. This latter distance is
then used to set the similarity threshold which will be applied to decide whether an
unseen object is detected or not. This strategy makes possible to reduce the number of
cases that are necessary to recognize objects whose shapes can differ from each other
significantly. This reduction is also achieved by considering point correspondences
for the matching procedure. Instead of using point coincidences, which requires the
shapes to be superimposed as much as possible, point correspondences are established
to adopt a more permissive behavior. Point correspondences are obtained by considering
different scales, all rotations and all translations. The search for correspondences
is an original legal one-to-one mapping between the points of the case shape and the
points of the unseen object shape. For each mapping, the distance between the shapes
is computed. It is based on the Euclidean distances between corresponding points,
takes into account outliers, considers the maximum matching error and is normalized
to run between 0 and 1. The similarity measure is directly derived from the latter distance.
Experiments on spores of six fungal strains have been conducted and prove that
the proposed algorithm yields good results. It is also shown that if the objects are
located side by side or are overlapped, then the similarity threshold has to be manually
lowered to recognize object.
Both papers show the potential of point correspondence approaches to handle objects
with high shape variance. Potential applications are numerous and range from
microscope image analysis to satellite image processing. Useful details regarding the
acquisition of shapes from real images are also given which makes the papers valuable
for readers willing to implement the described approaches.