Outcomes, impacts, highlights, nuggets... whatever name they go by, these
short, novice-friendly research descriptions are just one of the ways the IMA
shares the achievements of its visitors with the scientific community and
strives to increase public appreciation of applied mathematics. We've
recently added links to some of our most intriguing stories to our
homepage to give visitors a glimpse of
some of the fascinating research connected with the IMA.
If your research has been influenced by a visit to the IMA,
whether as a workshop participant, long-term visitor, or postdoc, please
share your story with us!
Below we describe two outcomes of the IMA 2005–2006 thematic program
Imaging: a promising new
algorithm in the highly competitive field of MRI brain imaging and a
novel approach to an age-old agricultural problem.
When viewed from the outside, a human brain appears as a volume
with a highly wrinkled surface having numerous long crevices.
Sulcal fundi are 3D curves that lie in the depths of the
informally, the fundus of a sulcus is the curve of maximal
average depth that spans the length of the sulcus.
The sulcal fundi serve as anatomical landmarks, 'segmenting'
the cortex into functionally distinct regions. They
are often used as landmarks for downstream computations in
and can be used in creating deformation fields for warping the
surfaces of different brains onto one another.
Cortical sulci and sulcal fundi have traditionally been
manually identified by
labeling voxels in an MRI brain volume using a GUI that
displays only three
orthogonal 2D brain slices. This process is extremely tedious
consuming and, not surprisingly, prone to human error.
Given the large number of high resolution MRI datasets
available for analysis, automatic and objective extraction and
cortical sulci has become a necessity. IMA industrial
postdoc Chiu Yen Kao and collaborators Michael Hofer (TU
Guillermo Sapiro (Minnesota), Josh Stern (Minnesota), and
(University of Minnesota and VA Medical Center),
have developed an automatic sulcal extraction method that
improve the quality and
reproducibility of the process as well as yielding considerable
An outer hull surface is computed from a mesh representation
of the graymatter surface by applying a
morphological closing operation to the level set function.
After the outer hull surface is obtained, the
geodesic depth (distance) for any given point on the pial
to the outer hull surface is calculated. This results in
the association of a sulcal depth estimate with each mesh
the sulcal regions are determined using a depth threshold of
The connected components are identified using a labeling
and the results are run through a thinning algorithm, yielding
a skeleton of
each connected component. The extracted sulcal fundi are
polylines that are further smoothed by an algorithm that
counterpart to the cubic spline energy for curves on surfaces.
An eye for aphids.
Soybeans are a key livestock feed in the US, an important human food source
in many parts of the world, and–in the form of biodiesel fuel–a
promising source of renewable energy. Informed pest management increases
yield and reduces pesticide application: farmers use population estimates
obtained by counting the aphids on sample soybean leaves in planning
their crop dusting schedules. However, manual aphid counts are very slow and
this low tech problem presents formidable challenges to even the most
sophisticated automatic image segmentation methods:
the colors of aphids change as the leaves age, with the color of
the aphids on young leaves nearly matching that of leaf veins; the intricate
structure of the veins and the tendency of aphids to cluster near veins
further complicate automated image segmentation.
In mid-February 2006, Martin DuSaire of the USDA contacted the IMA asking for
help in using new imaging techniques to obtain accurate counts of aphids on
soybean leaves. Long-term visitor Chang-Ock Lee (KAIST)
and his graduate student Jooyoung Hahn responded to the challenge by optimizing
their segmentation algorithm, which utilizes geometric attraction-driven flow
and edge regions, for soybean leaf images. The method involves a
geometric analysis of eigenspace in a tensor field on a color image as a
two-dimensional manifold and a statistical identification of
edge-regions; it requires neither interaction with end users nor
mid-process parameter manipulations. Within a few weeks, Lee and Hahn were
providing highly accurate, efficient aphid counts.