Efficient Detection of Second-Degree Variations in 2D and 3D Images

Danielsson, Per-Erik; Lin, Qingfen; Ye, Qin-Zhong

doi:10.1006/jvci.2000.0472

Cited by 47 publications

(26 citation statements)

References 31 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We note that, in the context of prolate spheroidal functions [38], and when constructing rotation invariant 2D filters [10], it has been observed that the (integer) symmetry order n of the function hðÞ expðinÞ where h is a one-dimensional function, and are polar coordinates, is preserved under the Fourier transform. To be precise, the Fourier transform of such functions are: H 0 ½hðÞð!…”

Section: F ½à Fp;mentioning

confidence: 89%

Recognition by symmetry derivatives and the generalized structure tensor

Bigün

Bigun²,

Nilsson

2004

IEEE Trans. Pattern Anal. Machine Intell.

119

View full text Add to dashboard Cite

Abstract-We suggest a set of complex differential operators that can be used to produce and filter dense orientation (tensor) fields for feature extraction, matching, and pattern recognition. We present results on the invariance properties of these operators, that we call symmetry derivatives. These show that, in contrast to ordinary derivatives, all orders of symmetry derivatives of Gaussians yield a remarkable invariance: They are obtained by replacing the original differential polynomial with the same polynomial, but using ordinary coordinates x and y corresponding to partial derivatives. Moreover, the symmetry derivatives of Gaussians are closed under the convolution operator and they are invariant to the Fourier transform. The equivalent of the structure tensor, representing and extracting orientations of curve patterns, had previously been shown to hold in harmonic coordinates in a nearly identical manner. As a result, positions, orientations, and certainties of intricate patterns, e.g., spirals, crosses, parabolic shapes, can be modeled by use of symmetry derivatives of Gaussians with greater analytical precision as well as computational efficiency. Since Gaussians and their derivatives are utilized extensively in image processing, the revealed properties have practical consequences for local orientation based feature extraction. The usefulness of these results is demonstrated by two applications: 1) tracking cross markers in long image sequences from vehicle crash tests and 2) alignment of noisy fingerprints.

show abstract

Section: F ½à Fp;mentioning

confidence: 89%

Recognition by symmetry derivatives and the generalized structure tensor

Bigün

Bigun²,

Nilsson

2004

IEEE Trans. Pattern Anal. Machine Intell.

119

View full text Add to dashboard Cite

show abstract

“…Sonka et al, 2008), see Fig. 5 (a), and the line detector by Danielsson (with σ = 1 pixel) (Danielsson, Lin & Ye, 2001), see Fig. 5 (b).…”

Section: Detection Of the Cell Wall Boundarymentioning

confidence: 99%

Automatic measurement of compression wood cell attributes in fluorescence microscopy images

Selig

Hendriks

Bardage³

et al. 2012

Journal of Microscopy

View full text Add to dashboard Cite

SummaryThis paper presents a new automated method for analyzing compression wood fibers in fluorescence microscopy. Abnormal wood known as compression wood is present in almost every softwood tree harvested. Compression wood fibers show a different cell wall morphology and chemistry compared to normal wood fibers, and their mechanical and physical characteristics are considered detrimental for both construction wood and pulp and paper purposes. Currently there is the need for improved methodologies for characterization of lignin distribution in wood cell walls, such as from compression wood fibers, that will allow for a better understanding of fiber mechanical properties. Traditionally, analysis of fluorescence microscopy images of fiber crosssections has been done manually, which is time consuming and subjective. Here, we present an automatic method, using digital image analysis, that detects and delineates softwood fibers in fluorescence microscopy images, dividing them into cell lumen, normal and highly lignified areas. It also quantifies the different areas, as well as measures cell wall thickness. The method is evaluated by comparing the automatic with a manual delineation. While the boundaries between the various fiber wall regions are detected using the automatic method with precision similar to inter and intra expert variability, the position of the boundary between lumen and the cell wall has a systematic shift that can be corrected. Our method allows for transverse structural characterization of compression wood fibers, which may allow for improved understanding of the micro-mechanical modeling of wood and pulp fibers.

show abstract

“…Local orientation can also be estimated by means of directional mathematical operations (Soille and Talbot, 1998;, or in the Fourier domain by examination of the energy of the power spectrum affected by appropriate orientation-selective linear filter (Kass and Witkin, 1987). The estimation of the second order derivatives (Danielsson et al, 2001), can be used to enhance and filter oriented structure (Perona and Malik, 1990;Frangi et al, 1998;Sato et al, 1998). However in what follows we will make only use of first order derivatives, less sensitive to noise.…”

Section: Principle Of Estimation Of the Local Orientation In Imagesmentioning

confidence: 99%

Segmentation of 2d and 3d Textures From Estimates of the Local Orientation

Jeulin¹,

Moreaud²

2011

Image Anal Stereol

View full text Add to dashboard Cite

We use a method to estimate local orientations in the n-dimensional space from the covariance matrix of the gradient, which can be implemented either in the image space or in the Fourier space. In a second step, two methods allow us to detect sudden changes of orientation in images. The first one uses an index of confidence of the estimated orientation, and the second one the detection of minima of scalar products in a neighbourhood. This is illustrated on 2D Transmission Electrons Microscope images of cellulose cryofracture (to display the organisation of cellulose whiskers and the points of germination), and to 3D images of a TA6V alloy (lamellar microstructure) obtained by microtomography.

show abstract

Efficient Detection of Second-Degree Variations in 2D and 3D Images

Cited by 47 publications

References 31 publications

Recognition by symmetry derivatives and the generalized structure tensor

Recognition by symmetry derivatives and the generalized structure tensor

Automatic measurement of compression wood cell attributes in fluorescence microscopy images

Segmentation of 2d and 3d Textures From Estimates of the Local Orientation

Contact Info

Product

Resources

About