MOTIVATION: Rotated template matching is an efficient and versatile algorithm to analyze microscopy images, as it automates the detection of stereotypical structures, such as organelles that can appear at any orientation. Its performance however quickly degrades in noisy image data. RESULTS: We introduce Steer'n'Detect, an ImageJ plugin implementing a recently published algorithm to detect patterns of interest at any orientation with high accuracy from a single template in 2D images. Steer'n'Detect provides a faster and more robust substitute to template matching. By adapting to the statistics of the image background, it guarantees accurate results even in the presence of noise. The plugin comes with an intuitive user interface facilitating results analysis and further post-processing. AVAILABILITY AND IMPLEMENTATION: https://github.com/Biomedical-Imaging-Group/Steer-n-Detect. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

We provide a complete pipeline for the detection of patterns of interest in an image. In our approach, the patterns are assumed to be adequately modeled by a known template, and are located at unknown positions and orientations that we aim at retrieving. We propose a continuous-domain additive image model, where the analyzed image is the sum of the patterns to localize and a background with self-similar isotropic power-spectrum. We are then able to compute the optimal filter fulfilling the SNR criterion based on one single template and background pair: it strongly responds to the template while being optimally decoupled from the background model. In addition, we constrain our filter to be steerable, which allows for a fast template detection together with orientation estimation. In practice, the implementation requires to discretize a continuous-domain formulation on polar grids, which is performed using quadratic radial B-splines. We demonstrate the practical usefulness of our method on a variety of template approximation and pattern detection experiments. We show that the detection performance drastically improves when we exploit the statistics of the background via its power-spectrum decay, which we refer to as spectral-shaping. The proposed scheme outperforms state-of-the-art steerable methods by up to 50% of absolute detection performance.

The detection of landmarks or patterns is of interest for extracting features in biological images. Hence, algorithms for finding these keypoints have been extensively investigated in the literature, and their localization and detection properties are well known. In this paper, we study the complementary topic of local orientation estimation, which has not received similar attention. Simply stated, the problem that we address is the following: estimate the angle of rotation of a pattern with steerable filters centered at the same location, where the image is corrupted by colored isotropic Gaussian noise. For this problem, we propose an estimator formulated as linear combinations of circular harmonics with given radial profiles. We prove that the proposed estimator is unbiased. This property allows us to use a statistical framework based on the Cramér--Rao lower bound (CRLB) to study the limits on the accuracy of the corresponding class of estimators. We aim at evaluating the performance of detection methods based on steerable filters in terms of angular accuracy (as a lower bound), while considering the connection to maximum likelihood estimation. Beyond the general results, we analyze the asymptotic behavior of the lower bound in terms of the order of steerablility and propose an optimal subset of components that minimizes the bound. We define a mechanism for selecting optimal subspaces of the span of the detectors. These are characterized by the most relevant angular frequencies. Finally, we project our template to the span of circular harmonics with given radial profiles and experimentally show that the prediction accuracy achieves the predicted CRLB. As an extension, we also consider steerable wavelet detectors.

We present texture operators encoding class-specific local organizations of image directions (LOIDs) in a rotation-invariant fashion. The LOIDs are key for visual understanding, and are at the origin of the success of the popular approaches, such as local binary patterns (LBPs) and the scale-invariant feature transform (SIFT). Whereas, LBPs and SIFT yield hand-crafted image representations, we propose to learn data-specific representations of the LOIDs in a rotation-invariant fashion. The image operators are based on steerable circular harmonic wavelets (CHWs), offering a rich and yet compact initial representation for characterizing natural textures. The joint location and orientation required to encode the LOIDs is preserved by using moving frames (MFs) texture representations built from locally-steered image gradients that are invariant to rigid motions. In a second step, we use support vector machines to learn a multi-class shaping matrix for the initial CHW representation, yielding data-driven MFs called steerable wavelet machines (SWMs). The SWM forward function is composed of linear operations (i.e., convolution and weighted combinations) interleaved with non-linear steermax operations. We experimentally demonstrate the effectiveness of the proposed operators for classifying natural textures. Our scheme outperforms recent approaches on several test suites of the Outex and the CUReT databases.

MOTIVATION: SpotCaliper is a novel wavelet-based image-analysis software providing a fast automatic detection scheme for circular patterns (spots), combined with the precise estimation of their size. It is implemented as an ImageJ plugin with a friendly user interface. The user is allowed to edit the results by modifying the measurements (in a semi-automated way), extract data for further analysis. The fine tuning of the detections includes the possibility of adjusting or removing the original detections, as well as adding further spots. RESULTS: The main advantage of the software is its ability to capture the size of spots in a fast and accurate way. AVAILABILITY AND IMPLEMENTATION: http://bigwww.epfl.ch/algorithms/spotcaliper/ CONTACT: [email protected] SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

In analogy with steerable wavelets, we present a general construction of adaptable tight wavelet frames, with an emphasis on scaling operations. In particular, the derived wavelets can be “dilated” by a procedure comparable to the operation of steering steerable wavelets. The fundamental aspects of the construction are the same: an admissible collection of Fourier multipliers is used to extend a tight wavelet frame, and the “scale” of the wavelets is adapted by scaling the multipliers. As an application, the proposed wavelets can be used to improve the frequency localization. Importantly, the localized frequency bands specified by this construction can be scaled efficiently using matrix multiplication.

We propose a framework for the detection of junctions in images. Although the detection of edges and key points is a well examined and described area, the multiscale detection of junction centers, especially for odd orders, poses a challenge in pattern analysis. The goal of this paper is to build optimal junction detectors based on 2D steerable wavelets that are polar-separable in the Fourier domain. The approaches we develop are general and can be used for the detection of arbitrary symmetric and asymmetric junctions. The backbone of our construction is a multiscale pyramid with a radial wavelet function where the directional components are represented by circular harmonics and encoded in a shaping matrix. We are able to detect M -fold junctions in different scales and orientations. We provide experimental results on both simulated and real data to demonstrate the effectiveness of the algorithm.

Our goal is to detect and group different kinds of local symmetries in images in a scale- and rotation-invariant way. We propose an efficient wavelet-based method to determine the order of local symmetry at each location. Our algorithm relies on circular harmonic wavelets which are used to generate steerable wavelet channels corresponding to different symmetry orders. To give a measure of local symmetry, we use the F-test to examine the distribution of the energy across different channels. We provide experimental results on synthetic images, biological micrographs, and electron-microscopy images to demonstrate the performance of the algorithm.