Rahul Jain | IISER Bhopal (original) (raw)

Papers by Rahul Jain

Cvgip: Image Understanding, 1991

The development of techniques for interpreting the structure of three-dimensional images, f(x,y,z... more The development of techniques for interpreting the structure of three-dimensional images, f(x,y,z), is useful in many applications. A key initial stage in the signal to symbol conversion process, essential for the interpretation of the data, is three-dimensional image segmentation involving the processes of partitioning and identification. Most segmentation and grouping research in computer vision has addressed partitioning of 2D images, f(x,y). In this paper, we present a parallel 3D image segmentation algorithm which, through the use of a-partitioning and volumejiltering, segments 3D images such that the greylevel variation within each volume can be described by a regression model. Experimental results demonstrate the effectiveness of this algorithm on several real-world 3D images. o tw Academic P~CSS. h.

Graphical Models /graphical Models and Image Processing /computer Vision, Graphics, and Image Processing, 1987

The location of a vanishing point determined by boundaries of a road indicates the direction of t... more The location of a vanishing point determined by boundaries of a road indicates the direction of the road. The detection of reliable road boundaries is a nontrivial task in most scenes, however. We propose an algorithm that uses hypothesized vanishing points to extract the road boundaries. Based on the direction and strength of edges in an area for a hypothesized vanishing point, a performance measure is computed. This performance measure reflects confidence in the hypothesis that the given vanishing point is the correct vanishing point for the road. The vanishing point for the given image, and the corresponding road boundaries is selected by searching for the maxima of the performance measures. The efficacy of our approach is demonstrated using several real-world road images.

for computing some function f : {0, 1} n × {0, 1} n → Z. We show that the first message of P can ... more for computing some function f : {0, 1} n × {0, 1} n → Z. We show that the first message of P can be compressed to O(k) classical bits using prior entanglement if it carries at most k bits of information about the sender's input. This implies a general direct sum result for one-round and simultaneous quantum protocols. It also implies a new round elimination lemma in quantum communication, which allows us to extend recent classical lower bounds on the cell probe complexity of some data structure problems, e.g. approximate nearest neighbor searching on the Hamming cube {0, 1} n , to the quantum setting. We then show an optimal tradeoff between the privacy losses of Alice and Bob in computing f in terms of the one-round quantum communication complexity of f with prior entanglement. This tradeoff is independent of the number of rounds of communication.

We prove a theorem about the relative entropy of quantum states, which roughly states that if the... more We prove a theorem about the relative entropy of quantum states, which roughly states that if the relative entropy, S(ρ σ) ∆ = Tr ρ(log ρ − log σ), of two quantum states ρ and σ is at most c, then ρ/2 O(c) 'sits inside' σ. Using this 'substate' theorem, we give tight lower bounds for the privacy loss of bounded error quantum communication protocols for the index function problem. We also give tight lower bounds for the k-round bounded error quantum communication complexity of the pointer chasing chasing problem, when the wrong player starts, and all the log n bits of the kth pointer are desired.

IEEE Transactions on Automatic Control, 2004

We consider a simple one-dimensional system whose observations are sent to a state estimator over... more We consider a simple one-dimensional system whose observations are sent to a state estimator over a noisy binary communication link. The interesting thing about the system is that it is unstable. The problem is to design an encoding scheme and a decoder such that the estimation error is stable. We explicitly construct a simple but efficient estimator for the binary symmetric channel (BSC). We are not aware of any such previous "codes" for the BSC. We compare our results to the nonconstructive bounds of Sahai.

We consider variations of the simplest one-dimensional linear control system in which communicati... more We consider variations of the simplest one-dimensional linear control system in which communication between the sensor and the controller is constrained by a binary communication channel. The link between the controller and the plant is not constrained. We study the limits imposed by the channel on the controller's ability to estimate the state and achieve stability. For discrete-time systems, several such limits have been published in the literature. We first derive these limits as bounds on the state transition matrix of the linear system then we investigate extensions for the cases (1) unknown initial conditions, (2) unknown state transition matrix and (3) noisy binary communication channels. For continuous-time systems, we consider a binary queue as the communication link. For this case, we also derive the bounds on the gain matrix of the linear. system. To our knowledge this is the first time a binary queue has been studied as the communication link in the proposed setting.

We show lower bounds in the multi-party quantum communication complexity model. In this model, th... more We show lower bounds in the multi-party quantum communication complexity model. In this model, there are

Let X and Y be finite non-empty sets and (X, Y ) a pair of random variables taking values in X × ... more Let X and Y be finite non-empty sets and (X, Y ) a pair of random variables taking values in X × Y. We consider communication protocols between two parties, ALICE and BOB, for generating X and Y . ALICE is provided an x ∈ X generated according to the distribution of X, and is required to send a message to BOB in order to enable him to generate y ∈ Y, whose distribution is the same as that of Y |X=x. Both parties have access to a shared random string generated in advance. Let T [X : Y ] be the minimum (over all protocols) of the expected number of bits ALICE needs to transmit to achieve this. We show that

Computing Research Repository, 2003

We prove lower bounds for the direct sum problem for two-party bounded error randomised multipler... more We prove lower bounds for the direct sum problem for two-party bounded error randomised multipleround communication protocols. Our proofs use the notion of information cost of a protocol, as defined by Chakrabarti et al. and refined further by . Our main technical result is a 'compression' theorem saying that, for any probability distribution £ over the inputs, a ¤ -round private coin bounded error protocol for a function ¥ with information cost ¦ can be converted into a ¤ round deterministic protocol for ¥ with bounded distributional error and communication cost § © ¤ ¦

Cvgip: Image Understanding, 1991

The development of techniques for interpreting the structure of three-dimensional images, f(x,y,z... more The development of techniques for interpreting the structure of three-dimensional images, f(x,y,z), is useful in many applications. A key initial stage in the signal to symbol conversion process, essential for the interpretation of the data, is three-dimensional image segmentation involving the processes of partitioning and identification. Most segmentation and grouping research in computer vision has addressed partitioning of 2D images, f(x,y). In this paper, we present a parallel 3D image segmentation algorithm which, through the use of a-partitioning and volumejiltering, segments 3D images such that the greylevel variation within each volume can be described by a regression model. Experimental results demonstrate the effectiveness of this algorithm on several real-world 3D images. o tw Academic P~CSS. h.

Graphical Models /graphical Models and Image Processing /computer Vision, Graphics, and Image Processing, 1987

The location of a vanishing point determined by boundaries of a road indicates the direction of t... more The location of a vanishing point determined by boundaries of a road indicates the direction of the road. The detection of reliable road boundaries is a nontrivial task in most scenes, however. We propose an algorithm that uses hypothesized vanishing points to extract the road boundaries. Based on the direction and strength of edges in an area for a hypothesized vanishing point, a performance measure is computed. This performance measure reflects confidence in the hypothesis that the given vanishing point is the correct vanishing point for the road. The vanishing point for the given image, and the corresponding road boundaries is selected by searching for the maxima of the performance measures. The efficacy of our approach is demonstrated using several real-world road images.

for computing some function f : {0, 1} n × {0, 1} n → Z. We show that the first message of P can ... more for computing some function f : {0, 1} n × {0, 1} n → Z. We show that the first message of P can be compressed to O(k) classical bits using prior entanglement if it carries at most k bits of information about the sender's input. This implies a general direct sum result for one-round and simultaneous quantum protocols. It also implies a new round elimination lemma in quantum communication, which allows us to extend recent classical lower bounds on the cell probe complexity of some data structure problems, e.g. approximate nearest neighbor searching on the Hamming cube {0, 1} n , to the quantum setting. We then show an optimal tradeoff between the privacy losses of Alice and Bob in computing f in terms of the one-round quantum communication complexity of f with prior entanglement. This tradeoff is independent of the number of rounds of communication.

We prove a theorem about the relative entropy of quantum states, which roughly states that if the... more We prove a theorem about the relative entropy of quantum states, which roughly states that if the relative entropy, S(ρ σ) ∆ = Tr ρ(log ρ − log σ), of two quantum states ρ and σ is at most c, then ρ/2 O(c) 'sits inside' σ. Using this 'substate' theorem, we give tight lower bounds for the privacy loss of bounded error quantum communication protocols for the index function problem. We also give tight lower bounds for the k-round bounded error quantum communication complexity of the pointer chasing chasing problem, when the wrong player starts, and all the log n bits of the kth pointer are desired.

IEEE Transactions on Automatic Control, 2004

We consider a simple one-dimensional system whose observations are sent to a state estimator over... more We consider a simple one-dimensional system whose observations are sent to a state estimator over a noisy binary communication link. The interesting thing about the system is that it is unstable. The problem is to design an encoding scheme and a decoder such that the estimation error is stable. We explicitly construct a simple but efficient estimator for the binary symmetric channel (BSC). We are not aware of any such previous "codes" for the BSC. We compare our results to the nonconstructive bounds of Sahai.

We consider variations of the simplest one-dimensional linear control system in which communicati... more We consider variations of the simplest one-dimensional linear control system in which communication between the sensor and the controller is constrained by a binary communication channel. The link between the controller and the plant is not constrained. We study the limits imposed by the channel on the controller's ability to estimate the state and achieve stability. For discrete-time systems, several such limits have been published in the literature. We first derive these limits as bounds on the state transition matrix of the linear system then we investigate extensions for the cases (1) unknown initial conditions, (2) unknown state transition matrix and (3) noisy binary communication channels. For continuous-time systems, we consider a binary queue as the communication link. For this case, we also derive the bounds on the gain matrix of the linear. system. To our knowledge this is the first time a binary queue has been studied as the communication link in the proposed setting.

We show lower bounds in the multi-party quantum communication complexity model. In this model, th... more We show lower bounds in the multi-party quantum communication complexity model. In this model, there are

Let X and Y be finite non-empty sets and (X, Y ) a pair of random variables taking values in X × ... more Let X and Y be finite non-empty sets and (X, Y ) a pair of random variables taking values in X × Y. We consider communication protocols between two parties, ALICE and BOB, for generating X and Y . ALICE is provided an x ∈ X generated according to the distribution of X, and is required to send a message to BOB in order to enable him to generate y ∈ Y, whose distribution is the same as that of Y |X=x. Both parties have access to a shared random string generated in advance. Let T [X : Y ] be the minimum (over all protocols) of the expected number of bits ALICE needs to transmit to achieve this. We show that

Computing Research Repository, 2003

We prove lower bounds for the direct sum problem for two-party bounded error randomised multipler... more We prove lower bounds for the direct sum problem for two-party bounded error randomised multipleround communication protocols. Our proofs use the notion of information cost of a protocol, as defined by Chakrabarti et al. and refined further by . Our main technical result is a 'compression' theorem saying that, for any probability distribution £ over the inputs, a ¤ -round private coin bounded error protocol for a function ¥ with information cost ¦ can be converted into a ¤ round deterministic protocol for ¥ with bounded distributional error and communication cost § © ¤ ¦