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Efficient grasping from rgbd images: Learning using a new rectangle representation
 In IEEE Int’l Conference on Robotics and Automation
, 2011
"... Abstract — Given an image and an aligned depth map of an object, our goal is to estimate the full 7dimensional gripper configuration—its 3D location, 3D orientation and the gripper opening width. Recently, learning algorithms have been successfully applied to grasp novel objects—ones not seen by th ..."
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Abstract — Given an image and an aligned depth map of an object, our goal is to estimate the full 7dimensional gripper configuration—its 3D location, 3D orientation and the gripper opening width. Recently, learning algorithms have been successfully applied to grasp novel objects—ones not seen by the robot before. While these approaches use lowdimensional representations such as a ‘grasping point ’ or a ‘pair of points’ that are perhaps easier to learn, they only partly represent the gripper configuration and hence are suboptimal. We propose to learn a new ‘grasping rectangle ’ representation: an oriented rectangle in the image plane. It takes into account the location, the orientation as well as the gripper opening width. However, inference with such a representation is computationally expensive. In this work, we present a two step process in which the first step prunes the search space efficiently using certain features that are fast to compute. For the remaining few cases, the second step uses advanced features to accurately select a good grasp. In our extensive experiments, we show that our robot successfully uses our algorithm to pick up a variety of novel objects. I.
Selecting Sums in Arrays
"... Abstract. In an array of n numbers each of the ` ´ ..."
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Algorithms for Finding the WeightConstrained k Longest Paths in a Tree and the LengthConstrained k MaximumSum Segments of a Sequence
, 2008
"... In this work, we obtain the following new results: – Given a tree T = (V, E) with a length function ℓ: E → R and a weight function w: E → R, a positive integer k, and an interval [L, U], the WeightConstrained k Longest Paths problem is to find the k longest paths among all paths in T with weights i ..."
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In this work, we obtain the following new results: – Given a tree T = (V, E) with a length function ℓ: E → R and a weight function w: E → R, a positive integer k, and an interval [L, U], the WeightConstrained k Longest Paths problem is to find the k longest paths among all paths in T with weights in the interval [L, U]. We show that the WeightConstrained k Longest Paths problem has a lower bound Ω(V log V + k) in the algebraic computation tree model and give an O(V log V + k)time algorithm for it. – Given a sequence A = (a1, a2,..., an) of numbers and an interval [L, U], we define the sum and length of a segment A[i, j] to be ai + ai+1 + · · · + aj and j − i + 1, respectively. The LengthConstrained k MaximumSum Segments problem is to find the k maximumsum segments among all segments of A with lengths in the interval [L, U]. We show that the LengthConstrained k MaximumSum Segments problem can be solved in O(n + k) time. ∗Corresponding
A Subcubic Time Algorithm for the kMaximum Subarray Problem
"... Abstract. We design a faster algorithm for the kmaximum subarray problem under the conventional RAM model, based on distance matrix multiplication (DMM). Specifically we achieve O(n 3 √ log log n/log n + k log n) for a general problem where overlapping is allowed for solution arrays. This complexi ..."
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Abstract. We design a faster algorithm for the kmaximum subarray problem under the conventional RAM model, based on distance matrix multiplication (DMM). Specifically we achieve O(n 3 √ log log n/log n + k log n) for a general problem where overlapping is allowed for solution arrays. This complexity is subcubic when k = o(n 3 / log n). The best known complexities of this problem are O(n 3 + k log n), which is cubic when k = O(n 3 /log n), and O(kn 3 √ log log n / log n), which is subcubic when k = o ( √ log n / log log n). 1
Data Structures: Sequence Problems, Range Queries and Fault Tolerance
, 2010
"... The focus of this dissertation is on algorithms, in particular data structures that give provably efficient solutions for sequence analysis problems, range queries, and fault tolerant computing. The work presented in this dissertation is divided into three parts. In Part I we consider algorithms for ..."
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The focus of this dissertation is on algorithms, in particular data structures that give provably efficient solutions for sequence analysis problems, range queries, and fault tolerant computing. The work presented in this dissertation is divided into three parts. In Part I we consider algorithms for a range of sequence analysis problems that have risen from applications in pattern matching, bioinformatics, and data mining. On a high level, each problem is defined by a function and some constraints and the job at hand is to locate subsequences that score high with this function and are not invalidated by the constraints. Many variants and similar problems have been proposed leading to several different approaches and algorithms. We consider problems where the function is the sum of the elements in the sequence and the constraints only bound the length of the subsequences considered. We give optimal algorithms for several variants of the problem based on a simple idea and classic algorithms and data structures. In Part II we consider range query data structures. This a category of
Insertion and sorting in a sequence of numbers minimizing the maximum sum of a contiguous subsequence
 Journal of Discrete Algorithms
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Parallel version of the Generalized Multidimensional KMaximum Subarray Problem with CUDAbased Implementation
"... Abstract—The Maximum Subarray Problem (MSP) finds the segment of an array that has the maximum summation over all other combinations. The Ddimensional KMaximum Subarray Problem is a generalized version of MSP, which finds K maximum subarrays in a Ddimensional array. The main aim of this course pr ..."
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Abstract—The Maximum Subarray Problem (MSP) finds the segment of an array that has the maximum summation over all other combinations. The Ddimensional KMaximum Subarray Problem is a generalized version of MSP, which finds K maximum subarrays in a Ddimensional array. The main aim of this course project is to develop a parallel version for this generalized version of the MSP. This work involves analyzing a sequential lower bounded, O(N+K) algorithm for KMSP in 1D and then developing a CUDAbased implementation which is competitive with the sequential version. Even though the problem is highly sequential, the CUDA version achieves more than 13X of speedup in performance compared to the sequential for an array size
Algorithms for the Problems of LengthConstrained Heaviest Segments
"... Abstract. We present algorithms for lengthconstrained maximum sum segment and maximum density segment problems, in particular, and the problem of finding lengthconstrained heaviest segments, in general, for a sequence of real numbers. Given a sequence of n real numbers and two real parameters L an ..."
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Abstract. We present algorithms for lengthconstrained maximum sum segment and maximum density segment problems, in particular, and the problem of finding lengthconstrained heaviest segments, in general, for a sequence of real numbers. Given a sequence of n real numbers and two real parameters L and U (L 6 U), the maximum sum segment problem is to find a consecutive subsequence, called a segment, of length at least L and at most U such that the sum of the numbers in the subsequence is maximum. The maximum density segment problem is to find a segment of length at least L and at most U such that the density of the numbers in the subsequence is the maximum. For the first problem with nonuniform width there is an algorithm with time and space complexities in O(n). We present an algorithm with time complexity in O(n) and space complexity in O(U). For the second problem with nonuniform width there is a combinatorial solution with time complexity in O(n) and space complexity in O(U). We present a simple geometric algorithm