The Fourier-Argand Representation: An Optimal Basis of Steerable Patterns

A Principled Design of Image Representation: Towards Forensic Tasks

Image forensics is a rising topic as the trustworthy multimedia content is critical for modern society. Like other vision-related applications, forensic analysis relies heavily on the proper image representation. Despite the importance, current theoretical understanding for such representation remains limited, with varying degrees of neglect for its key role. For this gap, we attempt to investigate the forensic-oriented image representation as a distinct problem, from the perspectives of theory, implementation, and application. Our work starts from the abstraction of basic principles that the representation for forensics should satisfy, especially revealing the criticality of robustness, interpretability, and coverage. At the theoretical level, we propose a new representation framework for forensics, called dense invariant representation (DIR), which is characterized by stable description with mathematical guarantees. At the implementation level, the discrete calculation problems of DIR are discussed, and the corresponding accurate and fast solutions are designed with generic nature and constant complexity. We demonstrate the above arguments on the dense-domain pattern detection and matching experiments, providing comparison results with state-of-the-art descriptors. Also, at the application level, the proposed DIR is initially explored in passive and active forensics, namely copy-move forgery detection and perceptual hashing, exhibiting the benefits in fulfilling the requirements of such forensic tasks.

Steer'n'Detect: Fast 2D Template Detection with Accurate Orientation Estimation

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

https://github.com/Biomedical-Imaging-Group/Steer-n-Detect.

SUPPLEMENTARY INFORMATION

Supplementary material (Steer'n'Detect user manual) is available at Bioinformatics online.

Principled Design and Implementation of Steerable Detectors

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.