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Recognition of binding patterns common to a set of protein structure
 Lecture Notes in Computer Science, 3500:440
, 2005
"... Abstract. We present a novel computational method, MultiBind, for recognition of binding patterns common to a set of protein structures. It is the first method which performs a multiple alignment between protein binding sites in the absence of overall sequence, fold or binding partner similarity. Mu ..."
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Abstract. We present a novel computational method, MultiBind, for recognition of binding patterns common to a set of protein structures. It is the first method which performs a multiple alignment between protein binding sites in the absence of overall sequence, fold or binding partner similarity. MultiBind recognizes common spatial arrangements of physicochemical properties in the binding sites. These should be important for recognition of function, prediction of binding and drug design. We discuss the theoretical aspects of the computational problem of multiple structure alignment. This problem involves solving a 3D kpartite matching problem, which we show to be NPHard. The MultiBind method, applies an efficient Geometric Hashing technique to detect a potential set of multiple alignments of the given binding sites. To overcome the exponential number of possible multiple combinations it applies a very efficient filtering procedure which is heavily based on the selected scoring function. Our method guarantees detection of an approximate solution in terms of pattern proximity as well as cardinality of multiple alignment. We show applications of MultiBind to several biological targets. The method recognizes patterns which are responsible for binding small molecules such as estradiol, ATP/ANP and transition state analogues. The presented computational results agree with the available biological ones.
AIGER D.: Super4pcs: Fast global pointcloud registration via smart indexing
 In Symp. on Geometry Processing (2014
"... input model scan Q scan P SUPER 4PCS (without ICP) GLSbased matching points Figure 1: We present SUPER 4PCS, an optimal linear time outputsensitive global alignment algorithm that registers a pair of raw pointclouds in arbitrary initial poses. This example is particularly challenging as no distinc ..."
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input model scan Q scan P SUPER 4PCS (without ICP) GLSbased matching points Figure 1: We present SUPER 4PCS, an optimal linear time outputsensitive global alignment algorithm that registers a pair of raw pointclouds in arbitrary initial poses. This example is particularly challenging as no distinctive geometric features are available (see right inset) and color cues (not used) are confusing due to object shininess. SUPER 4PCS works even with low overlap (∼25%), and 20 % outlier margin. Results are shown without ICP refinement. The proposed method has linear complexity over the stateoftheart 4PCS, which has a quadratic time complexity. Data acquisition in largescale scenes regularly involves accumulating information across multiple scans. A common approach is to locally align scan pairs using Iterative Closest Point (ICP) algorithm (or its variants), but requires static scenes and small motion between scan pairs. This prevents accumulating data across multiple scan sessions and/or different acquisition modalities (e.g., stereo, depth scans). Alternatively, one can use a global registration algorithm allowing scans to be in arbitrary initial poses. The stateoftheart global registration algorithm, 4PCS, however has a quadratic time complexity in the number of data points. This vastly limits its applicability to acquisition of large environments. We present S UPER 4PCS for global pointcloud registration that is optimal, i.e., runs in linear time (in the number of data points) and is also output sensitive in the complexity of the alignment problem based on the (unknown) overlap across scan pairs. Technically, we map the algorithm as an âĂŸinstance problemâĂZ ́ and solve it efficiently using a smart indexing data organization. The algorithm is simple, memoryefficient, and fast. We demonstrate that S UPER 4PCS results in significant speedup over alternative approaches and allows unstructured efficient acquisition of scenes at scales previously not possible. Complete source code and datasets are available for research use at
Maximizing the Area of Overlap of two Unions Of Disks under rigid motion
, 2004
"... Let A and B be two sets of n resp. m (m n) disjoint unit disks in the plane. We consider the problem of nding a rigid motion of A that maximizes the total area of its overlap with B. The function describing the area of overlap is quite complex, even for combinatorially equivalent translations, ..."
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Cited by 5 (0 self)
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Let A and B be two sets of n resp. m (m n) disjoint unit disks in the plane. We consider the problem of nding a rigid motion of A that maximizes the total area of its overlap with B. The function describing the area of overlap is quite complex, even for combinatorially equivalent translations, and hence, we turn our attention to approximation algorithms. First, we give a deterministic (1 )approximation algorithm for the maximum area of overlap under rigid motion that runs in O((n ) log m)) time. If is the diameter of set A, we get an (1 )approximation in O( 3 ) time. Under the condition that the maximum is at least a constant fraction of the area of A, we give a probabilistic (1 ) approximation algorithm that runs in O((m m) time and succeeds with high probability. Our algorithms generalize to the case where A and B consist of possibly intersecting disks of different radii provided that (i) the ratio of the radii of any two disks in A[B is bounded, and (ii) within each set, the maximum number of disks with a nonempty intersection is bounded.
Exact and approximate Geometric Pattern Matching for point sets in the plane under similarity transformations
 CCCG
, 2007
"... ..."
Maximizing the Area of Overlap of two Unions of Disks under Rigid Motion ∗
"... Let A and B be two sets of n resp. m disjoint unit disks in the plane, with m ≥ n. We consider the problem of finding a translation or rigid motion of A that maximizes the total area of overlap with B. The function describing the area of overlap is quite complex, even for combinatorially equivalent ..."
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Let A and B be two sets of n resp. m disjoint unit disks in the plane, with m ≥ n. We consider the problem of finding a translation or rigid motion of A that maximizes the total area of overlap with B. The function describing the area of overlap is quite complex, even for combinatorially equivalent translations and, hence, we turn our attention to approximation algorithms. We give deterministic (1 − ɛ)approximation algorithms for translations and for rigid motions, which run in O((nm/ɛ 2) log(m/ɛ)) and O((n 2 m 2 /ɛ 3) log m)) time, respectively. For rigid motions, we can also compute a (1 − ɛ)approximation in O((m 2 n 4/3 ∆ 1/3 /ɛ 3) log n log m) time, where ∆ is the diameter of set A. Under the condition that the maximum area of overlap is at least a constant fraction of the area of A, we give a probabilistic (1 − ɛ)approximation algorithm for rigid motions that runs in O((m 2 /ɛ 4) log 2 (m/ɛ) log m) time and succeeds with high probability. Our results generalize to the case where A and B consist of possibly intersecting disks of different radii, provided that (i) the ratio of the radii of any two disks in A ∪ B is bounded, and (ii) within each set, the maximum number of disks with a nonempty intersection is bounded.
www.cs.uu.nl Maximizing the Area of Overlap of two Unions of Disks under Rigid Motion
, 2004
"... Let A and B be two sets of n resp. m (m n) disjoint unit disks in the plane. We consider the problem of nding a rigid motion of A that maximizes the total area of its overlap with B. The function describing the area of overlap is quite complex, even for combinatorially equivalent translations, and ..."
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Let A and B be two sets of n resp. m (m n) disjoint unit disks in the plane. We consider the problem of nding a rigid motion of A that maximizes the total area of its overlap with B. The function describing the area of overlap is quite complex, even for combinatorially equivalent translations, and hence, we turn our attention to approximation algorithms. First, we give a deterministic (1 )approximation algorithm for the maximum area of overlap under rigid motion that runs in O((n 2 m
New Approaches to Robust, PointBased Image Registration
"... We consider various algorithmic solutions to image registration based on the alignment of a set of feature points. We present a number of enhancements to a branchandbound algorithm introduced by Mount, Netanyahu, and Le Moigne (Pattern Recognition, Vol. 32, 1999, pp. 17–38), which presented a regi ..."
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We consider various algorithmic solutions to image registration based on the alignment of a set of feature points. We present a number of enhancements to a branchandbound algorithm introduced by Mount, Netanyahu, and Le Moigne (Pattern Recognition, Vol. 32, 1999, pp. 17–38), which presented a registration algorithm based on the partial Hausdorff distance. Our enhancements include a new distance measure, the discrete Gaussian mismatch, and a number of improvements and extensions to the above search algorithm. Both distance measures are robust to the presence of outliers, that is, data points from either set that do not match any point of the other set. We present experimental studies, which show that the new distance measure considered can provide significant improvements over the partial Hausdorff distance in instances where the number of outliers is not known in advance. These experiments also show that our other algorithmic improvements can offer tangible improvements. We demonstrate the algorithm’s efficacy by considering images involving different sensors and different spectral bands, both in a traditional framework and in a multiresolution framework.