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A computational approach to edge detection
 IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE
, 1986
"... This paper describes a computational approach to edge detection. The success of the approach depends on the definition of a comprehensive set of goals for the computation of edge points. These goals must be precise enough to delimit the desired behavior of the detector while making minimal assumpti ..."
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Cited by 4675 (0 self)
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assumptions about the form of the solution. We define detection and localization criteria for a class of edges, and present mathematical forms for these criteria as functionals on the operator impulse response. A third criterion is then added to ensure that the detector has only one response to a single edge
Smooth solutions of quasianalytic or ultraholomorphic equations
"... Abstract. In the first part of this work, we consider a polynomial ϕ(x, y) = y d +a1(x)y d−1 + · · ·+ad(x) whose coefficients aj belong to a DenjoyCarleman quasianalytic local ring E1(M). Assuming that E1(M) is stable under derivation, we show that if h is a germ of C ∞ function such that ϕ(x, h(x ..."
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Cited by 4 (0 self)
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Abstract. In the first part of this work, we consider a polynomial ϕ(x, y) = y d +a1(x)y d−1 + · · ·+ad(x) whose coefficients aj belong to a DenjoyCarleman quasianalytic local ring E1(M). Assuming that E1(M) is stable under derivation, we show that if h is a germ of C ∞ function such that ϕ(x, h(x)) = 0, then h belongs to E1(M). This extends a wellknown fact about realanalytic functions. We also show that the result fails in general for nonquasianalytic ultradifferentiable local rings. In the second part of the paper, we study a similar problem in the framework of ultraholomorphic functions on sectors of the Riemann surface of the logarithm. We obtain a result that includes suitable nonquasianalytic situations.
Smooth solution of the ccompressible NavierStokes . . .
, 1998
"... The barotropic compressible Navier]Stokes equations in an unbounded domain are studied. We prove the unique existence of the solution u, p of the system 1.1 in the Sobolev space H kq 3 = H kq 2 provided that the derivatives of the data of the problem are sufficiently small, where k G 0 is any integ ..."
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The barotropic compressible Navier]Stokes equations in an unbounded domain are studied. We prove the unique existence of the solution u, p of the system 1.1 in the Sobolev space H kq 3 = H kq 2 provided that the derivatives of the data of the problem are sufficiently small, where k G 0 is any
MonoSLAM: Realtime single camera SLAM
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 2007
"... Abstract—We present a realtime algorithm which can recover the 3D trajectory of a monocular camera, moving rapidly through a previously unknown scene. Our system, which we dub MonoSLAM, is the first successful application of the SLAM methodology from mobile robotics to the “pure vision ” domain of ..."
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Cited by 490 (26 self)
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an active approach to mapping and measurement, the use of a general motion model for smooth camera movement, and solutions for monocular feature initialization and feature orientation estimation. Together, these add up to an extremely efficient and robust algorithm which runs at 30 Hz with standard PC
BLOWUP OF SMOOTH SOLUTIONS FOR RELATIVISTIC EULER EQUATIONS
, 2005
"... Abstract. We study the singularity formation of smooth solutions of the relativistic Euler equations in (3 + 1)dimensional spacetime for both finite initial energy and infinite initial energy. For the finite initial energy case, we prove that any smooth solution, with compactly supported nontrivia ..."
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Cited by 2 (0 self)
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Abstract. We study the singularity formation of smooth solutions of the relativistic Euler equations in (3 + 1)dimensional spacetime for both finite initial energy and infinite initial energy. For the finite initial energy case, we prove that any smooth solution, with compactly supported non
Smooth Solutions of the Three Dimensional NavierStokes Problem
, 2008
"... The aim of this paper is to solve the three dimensional NavierStokes problem with conservative source term when the initial conditions are divergence and curl free. We use convolution methods with basic vector calculus to construct “well behaved ” smooth solutions of the initial boundary value prob ..."
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The aim of this paper is to solve the three dimensional NavierStokes problem with conservative source term when the initial conditions are divergence and curl free. We use convolution methods with basic vector calculus to construct “well behaved ” smooth solutions of the initial boundary value
Smooth Solutions of Iterative Functional Differential Equations
"... Proceedings, pp. 228—252 Iterative functional differential equations are equations involving derivatives and iterates of the unknown function. Over the past fifty years, they have attracted the attention of many people and qualitative properties of such equations have been reported. In particular, ..."
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, there are now a number of existence results for smooth solutions of these equations. In this note, we present some of these results and explain the techniques that are involved in their derivation.
Ricci Flow with Surgery on ThreeManifolds
"... This is a technical paper, which is a continuation of [I]. Here we verify most of the assertions, made in [I, §13]; the exceptions are (1) the statement that a 3manifold which collapses with local lower bound for sectional curvature is a graph manifold this is deferred to a separate paper, as the ..."
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Cited by 448 (2 self)
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, as the proof has nothing to do with the Ricci flow, and (2) the claim about the lower bound for the volumes of the maximal horns and the smoothness of the solution from some time on, which turned out to be unjustified, and, on the other hand, irrelevant for the other conclusions. The Ricci flow with surgery
Results 11  20
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9,666