Distance transforms for real-valued functions

Molchanov, Ilya; Terán, Pedro

doi:10.1016/s0022-247x(02)00719-9

Cited by 25 publications

(10 citation statements)

References 5 publications

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“…Image thresholding can be difficult in low SNR and nonstationary images but may be alleviated through the application of more complicated thresholding techniques 45 or via the gray-level distance transform. 46 In our case, the inverse CT makes gray-level threshold selection simple by placing the background on the negative side of zero and the foreground on the positive side of zero, allowing the threshold to always remain at zero. Although gray-level thresholding is simplified, CT denoising adds the step of selecting how many curvelet coefficients to use.…”

Section: Discussionmentioning

confidence: 99%

Computational segmentation of collagen fibers from second-harmonic generation images of breast cancer

et al. 2014

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Second-harmonic generation (SHG) imaging can help reveal interactions between collagen fibers and cancer cells. Quantitative analysis of SHG images of collagen fibers is challenged by the heterogeneity of collagen structures and low signal-to-noise ratio often found while imaging collagen in tissue. The role of collagen in breast cancer progression can be assessed post acquisition via enhanced computation. To facilitate this, we have implemented and evaluated four algorithms for extracting fiber information, such as number, length, and curvature, from a variety of SHG images of collagen in breast tissue. The image-processing algorithms included a Gaussian filter, SPIRAL-TV filter, Tubeness filter, and curvelet-denoising filter. Fibers are then extracted using an automated tracking algorithm called fiber extraction (FIRE). We evaluated the algorithm performance by comparing length, angle and position of the automatically extracted fibers with those of manually extracted fibers in twenty-five SHG images of breast cancer. We found that the curvelet-denoising filter followed by FIRE, a process we call CT-FIRE, outperforms the other algorithms under investigation. CT-FIRE was then successfully applied to track collagen fiber shape changes over time in an in vivo mouse model for breast cancer.

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Section: Discussionmentioning

confidence: 99%

Computational segmentation of collagen fibers from second-harmonic generation images of breast cancer

et al. 2014

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“…This function is called a grayscale image. Since the computation of the Euclidean distance transform only works for binary images, Molchanov and Teran [13] have extended the Euclidean distance transform to grayscale images. A grayscale image is divided into N binary subimages obtained using N thresholds τ i , i = 1...N .…”

Section: ) For Grayscale Imagesmentioning

confidence: 99%

“…In this work, an extension of this measure is adapted to grayscale images. In [13], Molchanov and Teran have extended the Euclidean distance transform to grayscale images. This work has enabled us to adapt our approach to structural non-binary images.…”

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confidence: 99%

Modeling a Local Dissimilarity Map With Weibull Distribution–Application to 2-Class and Multi-Class Image Classification

et al. 2022

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“…An alternative is founded when transforming each spectral band from an intensity based map to a metric based map where at each pixel the value is associated to both the initial intensity and the spatial relationships between the image structures. This objective can be achieved using the Molchanov grey-scale distance function [26] for each spectral band dist(F :,:,k ). The new covariance matrix V Morpho-3 ∈ M D,D (R) is now defined as: Figure 8 depicts the corresponding grey-scale distance function from three spectral band of a hyperspectral image.…”

Section: Distance Function Morphpcamentioning

confidence: 99%

Morphological Principal Component Analysis for Hyperspectral Image Analysis

Franchi

Angulo

2016

IJGI

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This article deals with the issue of reducing the spectral dimension of a hyperspectral image using principal component analysis (PCA). To perform this dimensionality reduction, we propose the addition of spatial information in order to improve the features that are extracted. Several approaches proposed to add spatial information are discussed in this article. They are based on mathematical morphology operators. These morphological operators are the area opening/closing, granulometries and grey-scale distance function. We name the proposed family of techniques the Morphological Principal Component Analysis (MorphPCA). Present approaches provide new feature spaces able to jointly handle the spatial and spectral information of hyperspectral images. They are computationally simple since the key element is the computation of an empirical covariance matrix which integrates simultaneously both spatial and spectral information. The performance of the different feature spaces is assessed for different tasks in order to prove their practical interest.

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Distance transforms for real-valued functions

Cited by 25 publications

References 5 publications

Computational segmentation of collagen fibers from second-harmonic generation images of breast cancer

Computational segmentation of collagen fibers from second-harmonic generation images of breast cancer

Modeling a Local Dissimilarity Map With Weibull Distribution–Application to 2-Class and Multi-Class Image Classification

Morphological Principal Component Analysis for Hyperspectral Image Analysis

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