Symmetry sensitivities of Derivative-of-Gaussian filters

We consider the measurement of image structure using linear filters, in particular derivative-of-Gaussian (DtG) filters, which are an important model of V1 simple cells and widely used in computer vision, and whether such measurements can determine local image symmetry. We show that even a single linear filter can be sensitive to a symmetry, in the sense that specific responses of the filter can rule it out. We state and prove a necessary and sufficient, readily computable, criterion for filter symmetry-sensitivity. We use it to show that the six filters in a second order DtG family have patterns of joint sensitivity which are distinct for 12 different classes of symmetry. This rich symmetry-sensitivity adds to the properties that make DtG filters well-suited for probing local image structure, and provides a set of landmark responses suitable to be the foundation of a nonarbitrary system of feature categories

Change in mammographic density across birth cohorts of Dutch breast cancer screening participants

Contains fulltext : 208976.pdf (publisher's version ) (Open Access

Mammographic texture resemblance generalizes as an independent risk factor for breast cancer

INTRODUCTION: Breast density has been established as a major risk factor for breast cancer. We have previously demonstrated that mammographic texture resemblance (MTR), recognizing the local texture patterns of the mammogram, is also a risk factor for breast cancer, independent of percent breast density. We examine if these findings generalize to another population. METHODS: Texture patterns were recorded in digitalized pre-diagnosis (3.7 years) film mammograms of a nested case–control study within the Dutch screening program (S1) comprising of 245 breast cancers and 250 matched controls. The patterns were recognized in the same study using cross-validation to form resemblance scores associated with breast cancer. Texture patterns from S1 were examined in an independent nested case–control study within the Mayo Mammography Health Study cohort (S2) of 226 cases and 442 matched controls: mammograms on average 8.5 years prior to diagnosis, risk factor information and percent mammographic density (PD) estimated using Cumulus were available. MTR scores estimated from S1, S2 and S1 + S2 (the latter two as cross-validations) were evaluated in S2. MTR scores were analyzed as both quartiles and continuously for association with breast cancer using odds ratios (OR) and adjusting for known risk factors including age, body mass index (BMI), and hormone usage. RESULTS: The mean ages of S1 and S2 were 58.0 ± 5.7 years and 55.2 ± 10.5 years, respectively. The MTR scores on S1 showed significant capability to discriminate cancers from controls (area under the operator characteristics curve (AUC) = 0.63 ± 0.02, P <0.001), which persisted after adjustment for PD. S2 showed an AUC of 0.63, 0.61, and 0.60 based on PD, MTR scores trained on S2, and MTR scores trained on S1, respectively. When adjusted for PD, MTR scores of S2 trained on S1 showed an association with breast cancer for the highest quartile alone: OR in quartiles of controls as reference; 1.04 (0.59 to 1.81); 0.95 (0.52 to 1.74); 1.84 (1.10 to 3.07) respectively. The combined continuous model with both PD and MTR scores based on S1 had an AUC of 0.66 ± 0.03. CONCLUSIONS: The local texture patterns associated with breast cancer risk in S1 were also an independent risk factor in S2. Additional textures identified in S2 did not significantly improve risk segregation. Hence, the textural patterns that indicated elevated risk persisted under differences in X-ray technology, population demographics, follow-up time and geography

Linear image reconstruction by Sobolev norms on the bounded domain

The reconstruction problem is usually formulated as a variational problem in which one searches for that image that minimizes a so called prior (image model) while insisting on certain image features to be preserved. When the prior can be described by a norm induced by some inner product on a Hilbert space the exact solution to the variational problem can be found by orthogonal projection. In previous work we considered the image as compactly supported in and we used Sobolev norms on the unbounded domain including a smoothing parameter ¿&gt;¿0 to tune the smoothness of the reconstruction image. Due to the assumption of compact support of the original image components of the reconstruction image near the image boundary are too much penalized. Therefore we minimize Sobolev norms only on the actual image domain, yielding much better reconstructions (especially for ¿¿»¿0). As an example we apply our method to the reconstruction of singular points that are present in the scale space representation of an image

A Robust Algorithm for Characterizing Anisotropic Local Structures

International audienceThis paper proposes a robust estimation and validation framework for characterizing local structures in a positive multi-variate continuous function approximated by a Gaussian-based model. The new solution is robust against data with large deviations from the model and margin-truncations induced by neighboring structures. To this goal, it unifies robust statistical estimation for parametric model fitting and multi-scale analysis based on continuous scale-space theory. The unification is realized by formally extending the mean shift-based density analysis towards continuous signals whose local structure is characterized by an anisotropic fully-parameterized covariance matrix. A statistical validation method based on analyzing residual error of the chi-square fitting is also proposed to complement this estimation framework. The strength of our solution is the aforementioned robustness. Experiments with synthetic 1D and 2D data clearly demonstrate this advantage in comparison with the gamma-normalized Laplacian approach [12] and the standard sample estimation approach [13, p.179]. The new framework is applied to 3D volumetric analysis of lung tumors. A 3D implementation is evaluated with high-resolution CT images of 14 patients with 77 tumors, including 6 part-solid or ground-glass opacity nodules that are highly non-Gaussian and clinically significant. Our system accurately estimated 3D anisotropic spread and orientation for 82% of the total tumors and also correctly rejected all the failures without any false rejection and false acceptance. This system processes each 32-voxel volume-of-interest by an average of two seconds with a 2.4GHz Intel CPU. Our framework is generic and can be applied for the analysis of blob-like structures in various other applications

Natural image profiles are most likely to be step edges

AbstractWe introduce Geometric Texton Theory (GTT), a theory of categorical visual feature classification that arises through consideration of the metamerism that affects families of co-localised linear receptive-field operators. A refinement of GTT that uses maximum likelihood (ML) to resolve this metamerism is presented. We describe a method for discovering the ML element of a metamery class by analysing a database of natural images. We apply the method to the simplest case––the ML element of a canonical metamery class defined by co-registering the location and orientation of profiles from images, and affinely scaling their intensities so that they have identical responses to 1-D, zeroth- and first-order, derivative of Gaussian operators. We find that a step edge is the ML profile. This result is consistent with our proposed theory of feature classification