Geometry-Limited Diffusion in the Characterization of Geometric Patches in Images

Whitaker, Ross T.

doi:10.1006/ciun.1993.1007

Cited by 34 publications

(11 citation statements)

References 14 publications

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“…This is accomplished by letting the scale for boundariness be defined not according to the time of a uniform diffusion equation (the variance of a Gaussian envelope) but according to the time of a variable-conductance diffusion equation. [25], where the conductance is monotonic decreasing with the medialnessbased boundariness. This behaves as though the space near object boundaries is stretched before the medialness measures are made.…”

Section: Boundariness-medialness Interactionsmentioning

confidence: 99%

“…Boundariness at a particular location x and scale a has typically been associated with variations in luminance about that location, i.e., with combinations of first or second partial derivatives in some direction u of the intensity function after convolution with a Gaussian with standard deviation o-(see [4], Sobel's method in [7], and [25]). However, there are many other possible cues to boundariness.…”

Section: Multiscale Geometry Detectorsmentioning

confidence: 99%

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Object shape before boundary shape: Scale-space medial axes

et al. 1994

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Abstract. Representing object shape in two or three dimensions has typically involved the description of the object boundary. This paper proposes a means for characterizing object structure and shape that avoids the need to find an explicit boundary. Rather, it operates directly from the imageintensity distribution in the object and its background, using operators that do indeed respond to "boundariness." It produces a sort of medial-axis description that recognizes that both axis location and object width must be defined according to a tolerance proportional to the object width. This generalized axis is called the multiscale medial axis 1 because it is defined as a curve or set of curves in scale space. It has all of the advantages of the traditional medial axis: representation of protrusions and indentations in the object, decomposition of object-curvature and object-width properties, identification of visually opposite points of the object, incorporation of size constancy and orientation independence, and association of boundary-shape properties with medial locations. It also has significant new advantages: it does not require a predetermination of exactly what locations are included in the object, it provides gross descriptions that are stable against image detail, and it can be used to identify subobjects and regions of boundary detail and to characterize their shape properties.

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Section: Boundariness-medialness Interactionsmentioning

confidence: 99%

Section: Multiscale Geometry Detectorsmentioning

confidence: 99%

Object shape before boundary shape: Scale-space medial axes

et al. 1994

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“…Several features indicate the boundaries of planar patches: step edges (gradient magnitude) of amplitude, step edges of range, and step edges in the surface normal. The smoothing process is a vector-valued, anisotropic diffusion [39] as described in [40,41]. The processing consists of solving a system of nonlinear, partial differential equations with each equation being a variable-conductance diffusion where the conductance is what ensures coupling with other equations.…”

Section: Geometric Diffusion and Watershedsmentioning

confidence: 99%

“…The k j 's are free parameters expressed in units of the root-mean-squared gradients of the terms with which they are associated [40,42]; for this work, we have used k 1 = 2, k 2 = 3, and k 3 = k 4 = k 5 = 10. Equation (7) is solved on the discrete image grid using finiteforward differences as described in the literature [39,40].…”

Section: Geometric Diffusion and Watershedsmentioning

confidence: 99%

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Indoor Scene Reconstruction from Sets of Noisy Range Images

Gregor

Whitaker

2001

Graphical Models

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Wavelet-based solution to anisotropic diffusion equation for edge detection

Fontaine

Basu

1998

Int. J. Imaging Syst. Technol.

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We consider the problem of detection of edges in an image by solving an anisotropic diffusion equation, which has the intrinsic property that low‐contrast regions are smoothed and high‐contrast ones are enhanced. Since wavelets are known to provide better representation of singularities (i.e., edges), a more efficient scheme than those suggested earlier for solving the diffusion equation is formulated in terms of wavelet expansions of the image. These expansions also provide a natural way of estimating the local contrast, and hence of implementing a space‐varying parameterization of the diffusion equation for improved performance. Our method can be viewed as a wavelet counterpart of standard spectral methods for solving partial differential equations. © 1998 John Wiley & Sons, Inc. Int J Imaging Syst Technol, 9, 356–368, 1998

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Geometry-Limited Diffusion in the Characterization of Geometric Patches in Images

Cited by 34 publications

References 14 publications

Object shape before boundary shape: Scale-space medial axes

Object shape before boundary shape: Scale-space medial axes

Indoor Scene Reconstruction from Sets of Noisy Range Images

Wavelet-based solution to anisotropic diffusion equation for edge detection

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