Ole Fogh Olsen

Scale-space theories in computer vision

Blurring is not the only way to selectively remove fine spatial detail from an image. An alternative is to scramble pixels locally over areas defined by the desired blur circle. We refer to such scrambled images as “locally disorderly”. Such images have many potentially interesting applications. In this contribution we discuss a formal framework for such locally disorderly images. It boils down to a number of intricately intertwined scale spaces, one of which is the ordinary linear scale space for the image. The formalism is constructed on the basis of an operational definition of local histograms of arbitrary bin width and arbitrary support.

Segmenting Articular Cartilage Automatically Using a Voxel Classification Approach

We present a fully automatic method for articular cartilage segmentation from magnetic resonance imaging (MRI) which we use as the foundation of a quantitative cartilage assessment. We evaluate our method by comparisons to manual segmentations by a radiologist and by examining the interscan reproducibility of the volume and area estimates. Training and evaluation of the method is performed on a data set consisting of 139 scans of knees with a status ranging from healthy to severely osteoarthritic. This is, to our knowledge, the only fully automatic cartilage segmentation method that has good agreement with manual segmentations, an interscan reproducibility as good as that of a human expert, and enables the separation between healthy and osteoarthritic populations. While high-field scanners offer high-quality imaging from which the articular cartilage have been evaluated extensively using manual and automated image analysis techniques, low-field scanners on the other hand produce lower quality images but to a fraction of the cost of their high-field counterpart. For low-field MRI, there is no well-established accuracy validation for quantitative cartilage estimates, but we show that differences between healthy and osteoarthritic populations are statistically significant using our cartilage volume and surface area estimates, which suggests that low-field MRI analysis can become a useful, affordable tool in clinical studies

Automatic segmentation of the articular cartilage in knee MRI using a hierarchical multi-class classification scheme

Osteoarthritis is characterized by the degeneration of the articular cartilage in joints. We have developed a fully automatic method for segmenting the articular cartilage in knee MR scans based on supervised learning. A binary approximate kNN classifier first roughly separates cartilage from background voxels, then a three-class classifier assigns one of three classes to each voxel that is classified as cartilage by the binary classifier. The resulting sensitivity and specificity are 90.0% and 99.8% respectively for the medial cartilage compartments. We show that an accurate automatic cartilage segmentation is achievable using a low-field MR scanner.

Multiscale Gradient Magnitude Watershed Segmentation

A partitioning of an nD image is defined as the watersheds of some locally computable inhomogeneity measure. Dependent on the scale of the inhomogeneity measure a coarse or fine partitioning is defined. By analysis of the structural changes (catastrophes) in the measure introduced when scale is increased, a multi-scale linking of segments can be defined. This paper describes the multi-scale linking based on recent results of the deep structure of the squared gradient field[1]. An interactive semi-automatic segmentation tool, and results on synthetic and real 3D medical images are presented.

Deep Structure, Singularities, and Computer Vision

Oral Presentations.- Blurred Correlation Versus Correlation Blur.- A Scale Invariant Covariance Structure on Jet Space.- Essential Loops and Their Relevance for Skeletons and Symmetry Sets.- Pre-symmetry Sets of 3D Shapes.- Deep Structure of Images in Populations Via Geometric Models in Populations.- Estimating the Statistics of Multi-object Anatomic Geometry Using Inter-object Relationships.- Histogram Statistics of Local Model-Relative Image Regions.- The Bessel Scale-Space.- Linear Image Reconstruction from a Sparse Set of ?-Scale Space Features by Means of Inner Products of Sobolev Type.- A Riemannian Framework for the Processing of Tensor-Valued Images.- From Stochastic Completion Fields to Tensor Voting.- Deep Structure from a Geometric Point of View.- Maximum Likely Scale Estimation.- Adaptive Trees and Pose Identification from External Contours of Polyhedra.- Poster Presentations.- Exploiting Deep Structure.- Scale-Space Hierarchy of Singularities.- Computing 3D Symmetry Sets A Case Study.- Irradiation Orientation from Obliquely Viewed Texture.- Using Top-Points as Interest Points for Image Matching.- Transitions of Multi-scale Singularity Trees.- A Comparison of the Deep Structure of ?-Scale Spaces.- A Note on Local Morse Theory in Scale Space and Gaussian Deformations.

Multi-Scale Watershed Segmentation

On the path from acquisition to interpretation of an image one of the biggest hurdles is segmentation. That is, partitioning the image into basic structures corresponding to meaningful objects. One of the goals in this chapter is to outline how a segmentation tool can be built on top of linear Gaussian scale space. Another goal is to show the usefulness of catastrophe theory for analysing the deep structure of features in scale space.

Automatic quantification of local and global articular cartilage surface curvature: Biomarkers for osteoarthritis?

The objective of this study was to quantitatively assess the surface curvature of the articular cartilage from low‐field magnetic resonance imaging (MRI) data, and to investigate its role in populations with varying radiographic signs of osteoarthritis (OA), cross‐sectionally and longitudinally. The curvature of the articular surface of the medial tibial compartment was estimated both on fine and coarse scales using two different automatic methods which are both developed from an automatic 3D segmentation algorithm. Cross‐sectionally (n = 288), the surface curvature for both the fine‐ and coarse‐scale estimates were significantly higher in the OA population compared with the healthy population, with P < 0.001 and P ≪ 0.001, respectively. For the longitudinal study (n = 245), there was a significant increase in fine‐scale curvature for healthy and borderline OA populations (P < 0.001), and in coarse‐scale curvature for severe OA populations (P < 0.05). Fine‐scale curvature could predict progressors using the estimates of those healthy at baseline (P < 0.001). The inter‐scan precision was 2.2 and 6.5 (mean CV) for the fine‐ and coarse scale curvature measures, respectively. The results showed that quantitative curvature estimates from low‐field MRI at different scales could potentially become biomarkers targeted at different stages of OA. Magn Reson Med 59:1340–1346, 2008.

Branch Points in One-Dimensional Gaussian Scale Space

AbstractScale space analysis combines global and local analysis in a single methodology by simplifying a signal. The simplification is indexed using a continuously varying parameter denoted scale. Different analyses can then be performed at their proper scale. We consider evolution of a polynomial by the parabolic partial differential heat equation. We first study a basis for the solution space, the heat polynomials, and subsequently the local geometry around a branch point in scale space. By a branch point of a polynomium we mean a scale and a location where two zeros of the polynomial merge. We prove that the number of branch points for a solution is

Diffusion Based Photon Mapping

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