Bereg, Sergey

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Dr. Bereg's research interests include:

  • Computational Biology and Bioinformatics
  • Computational Geometry and Geometric Optimization
  • Networks and Communications
  • Geographic Information Systems
  • Facility Location
  • Pattern Matching

You can learn more about Sergey Bereg on his home page and Research Explorer page.


Recent Submissions

Now showing 1 - 3 of 3
  • Item
    An Accurate Algorithm to Match Imperfectly Matched Images for Lung Tumor Detection without Markers
    (Multimed Inc) Rozario, Timothy; Bereg, Sergey; Yan, Yulong; Chiu, Tsuicheng; Liu, Honghuan; Kearney, Vasant; Jiang, Lan; Mao, Weihua
    In order to locate lung tumors on kV projection images without internal markers, digitally reconstructed radiographs (DRRs) are created and compared with projection images. However, lung tumors always move due to respiration and their locations change on projection images while they are static on DRRs. In addition, global image intensity discrepancies exist between DRRs and projections due to their different image orientations, scattering, and noises. This adversely affects comparison accuracy. A simple but efficient comparison algorithm is reported to match imperfectly matched projection images and DRRs. The kV projection images were matched with different DRRs in two steps. Preprocessing was performed in advance to generate two sets of DRRs. The tumors were removed from the planning 3D CT for a single phase of planning 4D CT images using planning contours of tumors. DRRs of background and DRRs of tumors were generated separately for every projection angle. The first step was to match projection images with DRRs of background signals. This method divided global images into a matrix of small tiles and similarities were evaluated by calculating normalized cross-correlation (NCC) between corresponding tiles on projections and DRRs. The tile configuration (tile locations) was automatically optimized to keep the tumor within a single projection tile that had a bad matching with the corresponding DRR tile. A pixel-based linear transformation was determined by linear interpolations of tile transformation results obtained during tile matching. The background DRRs were transformed to the projection image level and subtracted from it. The resulting subtracted image now contained only the tumor. The second step was to register DRRs of tumors to the subtracted image to locate the tumor. This method was successfully applied to kV fluoro images (about 1000 images) acquired on a Vero (BrainLAB) for dynamic tumor tracking on phantom studies. Radiation opaque markers were implanted and used as ground truth for tumor positions. Although other organs and bony structures introduced strong signals superimposed on tumors at some angles, this method accurately located tumors on every projection over 12 gantry angles. The maximum error was less than 2.2 mm, while the total average error was less than 0.9 mm. This algorithm was capable of detecting tumors without markers, despite strong background signals.
  • Item
    Balanced line for a 3-colored point set in the plane
    Bereg, Sergey; Kano, Mikio; Bereg, Sergey
    In this note we prove the following theorem. For any three sets of points in the plane, each of n ≥ 2 points such that any three points (from the union of three sets) are not collinear and the convex hull of 3n points is monochromatic, there exists an integer k ε {1, 2, ..., n-1} and an open half-plane containing exactly k points from each set.
  • Item
    On the coarseness of bicolored point sets
    (Elsevier B. V., 2012-04-24) Bereg, Sergey; Díaz-Báñez, J. M.; Lara, D.; Pérez-Lantero, P.; Seara, C.; Urrutia, J.; Bereg, Sergey
    Let R be a set of red points and B a set of blue points on the plane. In this paper we introduce a new concept, which we call coarseness, for measuring how blended the elements of S=R⊃B are. For X∪S, let Δ(X)=

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