Henrik Skibbe

Rotation-Invariant HOG Descriptors Using Fourier Analysis in Polar and Spherical Coordinates

The histogram of oriented gradients (HOG) is widely used for image description and proves to be very effective. In many vision problems, rotation-invariant analysis is necessary or preferred. Popular solutions are mainly based on pose normalization or learning, neglecting some intrinsic properties of rotations. This paper presents a method to build rotation-invariant HOG descriptors using Fourier analysis in polar/spherical coordinates, which are closely related to the irreducible representation of the 2D/3D rotation groups. This is achieved by considering a gradient histogram as a continuous angular signal which can be well represented by the Fourier basis (2D) or spherical harmonics (3D). As rotation-invariance is established in an analytical way, we can avoid discretization artifacts and create a continuous mapping from the image to the feature space. In the experiments, we first show that our method outperforms the state-of-the-art in a public dataset for a car detection task in aerial images. We further use the Princeton Shape Benchmark and the SHREC 2009 Generic Shape Benchmark to demonstrate the high performance of our method for similarity measures of 3D shapes. Finally, we show an application on microscopic volumetric data.

ViBE-Z: a framework for 3D virtual colocalization analysis in zebrafish larval brains.

Precise three-dimensional (3D) mapping of a large number of gene expression patterns, neuronal types and connections to an anatomical reference helps us to understand the vertebrate brain and its development. We developed the Virtual Brain Explorer (ViBE-Z), a software that automatically maps gene expression data with cellular resolution to a 3D standard larval zebrafish (Danio rerio) brain. ViBE-Z enhances the data quality through fusion and attenuation correction of multiple confocal microscope stacks per specimen and uses a fluorescent stain of cell nuclei for image registration. It automatically detects 14 predefined anatomical landmarks for aligning new data with the reference brain. ViBE-Z performs colocalization analysis in expression databases for anatomical domains or subdomains defined by any specific pattern; here we demonstrate its utility for mapping neurons of the dopaminergic system. The ViBE-Z database, atlas and software are provided via a web interface.

Fast Rotation Invariant 3D Feature Computation Utilizing Efficient Local Neighborhood Operators

We present a method for densely computing local rotation invariant image descriptors in volumetric images. The descriptors are based on a transformation to the harmonic domain, which we compute very efficiently via differential operators. We show that this fast voxelwise computation is restricted to a family of basis functions that have certain differential relationships. Building upon this finding, we propose local descriptors based on the Gaussian Laguerre and spherical Gabor basis functions and show how the coefficients can be computed efficiently by recursive differentiation. We exemplarily demonstrate the effectiveness of such dense descriptors in a detection and classification task on biological 3D images. In a direct comparison to existing volumetric features, among them 3D SIFT, our descriptors reveal superior performance.

SHOG: spherical HOG descriptors for rotation invariant 3D object detection

We present a method for densely computing local spherical histograms of oriented gradients (SHOG) in volumetric images. The descriptors are based on the continuous representation of the orientation histograms in the harmonic domain, which we compute very efficiently via spherical tensor products and the Fast Fourier Transformation. Building upon these local spherical histogram representations, we utilize the Harmonic Filter to create a generic rotation invariant object detection system that benefits from both the highly discriminative representation of local image patches in terms of histograms of oriented gradients and an adaptable trainable voting scheme that forms the filter. We exemplarily demonstrate the effectiveness of such dense spherical 3D descriptors in a detection task on biological 3D images. In a direct comparison to existing approaches, our new filter reveals superior performance.

Fast computation of 3D spherical Fourier harmonic descriptors - a complete orthonormal basis for a rotational invariant representation of three-dimensional objects

In this paper we propose to extend the well known spherical harmonic descriptors[6] (SHD) by adding an additional Fourier-like radial expansion to represent volumetric data. Having created an orthonormal basis on the ball with all the gentle properties known from the spherical harmonics theory and Fourier theory, we are able to compute efficiently a multi-scale representation of 3D objects that leads to highly discriminative rotation-invariant features, which will be called spherical Fourier harmonic descriptors (SFHD). Experiments on the challenging Princeton Shape Benchmark (PSB[16]) demonstrate the superiority of SFHD over the ordinary SHD.

3D object detection using a fast voxel-wise local spherical Fourier tensor transformation

In this paper we present a novel approach for expanding spherical 3D-tensor fields of arbitrary order in terms of a tensor valued local Fourier basis. For an efficient implementation, a two step approach is suggested combined with the use of spherical derivatives. Based on this new transformation we conduct two experiments utilizing the spherical tensor algebra for computing and using rotation invariant features for object detection and classification. The first experiment covers the successful detection of non-spherical root cap cells of Arabidopsis root tips presented in volumetric microscopical recordings. The second experiment shows how to use these features for successfully detecting a-helices in cryo-EM density maps of secondary protein structures, leading to very promising results.

Increasing the Dimension of Creativity in Rotation Invariant Feature Design Using 3D Tensorial Harmonics

Spherical harmonics are widely used in 3D image processing due to their compactness and rotation properties. For example, it is quite easy to obtain rotation invariance by taking the magnitudes of the representation, similar to the power spectrum known from Fourier analysis. We propose a novel approach extending the spherical harmonic representation to tensors of higher order in a very efficient manner. Our approach utilises the so called tensorial harmonics [1] to overcome the restrictions to scalar fields. In this way it is possible to represent vector and tensor fields with all the gentle properties known from spherical harmonic theory. In our experiments we have tested our system by using the most commonly used tensors in three dimensional image analysis, namely the gradient vector, the Hessian matrix and finally the structure tensor. For comparable results we have used the Princeton Shape Benchmark [2] and a database of airborne pollen, leading to very promising results.

Spherical Bessel Filter for 3D object detection

The detection of 3D objects and landmarks in arbitrary orientations is one of the most challenging tasks in biomedical 3D image analysis. In this paper we introduce the spherical Bessel Filter (BF) for rotation invariant 3D object detection tasks. The BF is based on the Harmonic Filter (HF) and thus inherits all the gentle properties of the HF, in particular the data driven adaptability and the processing speed. In contrast to the HF the BF benefits from a better object representation based on local spherical Fourier basis functions leading to noticeably better object detections and localizations.

3D Rotation-Invariant Description from Tensor Operation on Spherical HOG Field

Rotation-invariant descriptions are required in many 3D volumetric image analysis tasks. The histogram-of-oriented-gradient (HOG) is widely used in 2D images and proves to be a very robust local description. This paper concentrates on how to use the HOG feature in 3D volumetric images when rotation-invariance is concerned. This is challenging because of the complexity of 3D rotations. We present a decent solution based on the spherical harmonics theory which is an effective tool for analysing 3D rotations, together with the spherical tensor operations which explore high order tensor information in spherical coordinates. The design is quite general and could be used for different applications. It achieves high scores on Princeton Shape Benchmark and SHREC 2009 Generic Shape Benchmark, and also produces promising results when applying on biological microscopy images.

Image retrieval based on a multipurpose watermarking scheme

The rapid development of Internet and multimedia technologies has made copyright protection and multimedia retrieval be the two most important issues in the digital world. To solve these problems simultaneously, this paper presents a multipurpose watermarking scheme for image retrieval. First, several important features are computed offline for each image in the database. Then, the copyright, annotation and feature watermarks are offline embedded into all images in the database. During the online retrieval, the query image features are compared with the exacted features from each image in the database to find the similar images. The experimental results based on a database with 1000 images in 10 classes demonstrate the effectiveness of the proposed scheme.