A Computational Approach to Edge Detection
IEEE Transactions on Pattern Analysis and Machine Intelligence
Digital image processing (2nd ed.)
Digital image processing (2nd ed.)
Digital topology: introduction and survey
Computer Vision, Graphics, and Image Processing
Scale-Space and Edge Detection Using Anisotropic Diffusion
IEEE Transactions on Pattern Analysis and Machine Intelligence
Scale-Space for Discrete Signals
IEEE Transactions on Pattern Analysis and Machine Intelligence
Surface Parametrization and Curvature Measurement of Arbitrary 3-D Objects: Five Practical Methods
IEEE Transactions on Pattern Analysis and Machine Intelligence
A multi-scale approach to nonuniform diffusion
CVGIP: Image Understanding
3D digital topology under binary transformation with applications
Computer Vision and Image Understanding
IEEE Transactions on Pattern Analysis and Machine Intelligence
A Transform for Multiscale Image Segmentation by Integrated Edge and Region Detection
IEEE Transactions on Pattern Analysis and Machine Intelligence
Probabilistic Multiscale Image Segmentation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Local Scale Control for Edge Detection and Blur Estimation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Zoom-invariant vision of figural shape: the mathematics of cores
Computer Vision and Image Understanding
Scale-Space Derived From B-Splines
IEEE Transactions on Pattern Analysis and Machine Intelligence
On the Representation of Image Structures via Scale Space Entropy Conditions
IEEE Transactions on Pattern Analysis and Machine Intelligence
Scale-based fuzzy connected image segmentation: theory, algorithms, and validation
Computer Vision and Image Understanding - Special issue on analysis of volumetric image
Clustering by Scale-Space Filtering
IEEE Transactions on Pattern Analysis and Machine Intelligence
Scale-Space Theory in Computer Vision
Scale-Space Theory in Computer Vision
Effective Scale: A Natural Unit for Measuring Scale-Space Lifetime
IEEE Transactions on Pattern Analysis and Machine Intelligence
Fuzzy distance transform: theory, algorithms, and applications
Computer Vision and Image Understanding
ICCV '98 Proceedings of the Sixth International Conference on Computer Vision
A novel cubic-order algorithm for approximating principal direction vectors
ACM Transactions on Graphics (TOG)
The "Dead reckoning" signed distance transform
Computer Vision and Image Understanding
Recognition by Symmetry Derivatives and the Generalized Structure Tensor
IEEE Transactions on Pattern Analysis and Machine Intelligence
A Riemannian Framework for Tensor Computing
International Journal of Computer Vision
Image Processing, Analysis, and Machine Vision
Image Processing, Analysis, and Machine Vision
Computer Vision and Image Understanding
Shape feature extraction and description based on tensor scale
Pattern Recognition
IJCAI'83 Proceedings of the Eighth international joint conference on Artificial intelligence - Volume 2
Computer Vision and Image Understanding
Vectorial scale-based fuzzy-connected image segmentation
Computer Vision and Image Understanding
Generalized scale: Theory, algorithms, and application to image inhomogeneity correction
Computer Vision and Image Understanding
Image segmentation based on GrabCut framework integrating multiscale nonlinear structure tensor
IEEE Transactions on Image Processing
An Analytic Approach to Tensor Scale with an Efficient Algorithm and Applications to Image Filtering
DICTA '10 Proceedings of the 2010 International Conference on Digital Image Computing: Techniques and Applications
A novel method to look for the hysteresis thresholds for the Canny edge detector
Pattern Recognition
IEEE Transactions on Pattern Analysis and Machine Intelligence
Multiscale image segmentation by integrated edge and region detection
IEEE Transactions on Image Processing
Scale space classification using area morphology
IEEE Transactions on Image Processing
Nonlinear scale-space filtering and multiresolution system
IEEE Transactions on Image Processing
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Scale is a widely used notion in computer vision and image understanding that evolved in the form of scale-space theory where the key idea is to represent and analyze an image at various resolutions. Recently, we introduced a notion of local morphometric scale referred to as ''tensor scale'' using an ellipsoidal model that yields a unified representation of structure size, orientation and anisotropy. In the previous work, tensor scale was described using a 2-D algorithmic approach and a precise analytic definition was missing. Also, the application of tensor scale in 3-D using the previous framework is not practical due to high computational complexity. In this paper, an analytic definition of tensor scale is formulated for n-dimensional (n-D) images that captures local structure size, orientation and anisotropy. Also, an efficient computational solution in 2- and 3-D using several novel differential geometric approaches is presented and the accuracy of results is experimentally examined. Also, a matrix representation of tensor scale is derived facilitating several operations including tensor field smoothing to capture larger contextual knowledge. Finally, the applications of tensor scale in image filtering and n-linear interpolation are presented and the performance of their results is examined in comparison with respective state-of-art methods. Specifically, the performance of tensor scale based image filtering is compared with gradient and Weickert's structure tensor based diffusive filtering algorithms. Also, the performance of tensor scale based n-linear interpolation is evaluated in comparison with standard n-linear and windowed-sinc interpolation methods.