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.

Accurate identification of protein secondary structures is beneficial to understand three-dimensional structures of biological macromolecules. In this paper, a novel refined classification framework is proposed, which treats alpha-helix identification as a machine learning problem by representing each voxel in the density map with its Spherical Harmonic Descriptors (SHD). An energy function is defined to provide statistical analysis of its identification performance, which can be applied to all the α-helix identification approaches. Comparing with other existing α-helix identification methods for intermediate resolution electron density maps, the experimental results demonstrate that our approach gives the best identification accuracy and is more robust to the noise.

We propose an algorithm for 3-D multiview deblurring using spatially variant point spread functions (PSFs). The algorithm is applied to multiview reconstruction of volumetric microscopy images. It includes registration and estimation of the PSFs using irregularly placed point markers (beads). We formulate multiview deblurring as an energy minimization problem subject to L1-regularization. Optimization is based on the regularized Lucy-Richardson algorithm, which we extend to deal with our more general model. The model parameters are chosen in a profound way by optimizing them on a realistic training set. We quantitatively and qualitatively compare with existing methods and show that our method provides better signal-to-noise ratio and increases the resolution of the reconstructed images.

Gradient vector flow snakes are a very common method in bio-medical image segmentation. The use of gradient vector flow herein brings some major advantages like a large capture range and a good adaption of the snakes in concave regions. In some cases though, the application of gradient vector flow can also have undesired effects, e.g. if only parts of an image are strongly blurred, the remaining weak gradients will be smoothed away. Also, large gradients resulting from small but bright image structures usually have strong impact on the overall result. To tackle this problem, we present an improvement of the gradient vector flow, using the mean shift procedure and show its advantages on the segmentation of 3D cell nuclei.

When using deformable models for the segmentation of biological data, the choice of the best weighting parameters for the internal and external forces is crucial. Especially when dealing with 3D fluorescence microscopic data and cells within dense tissue, object boundaries are sometimes not visible. In these cases, one weighting parameter set for the whole contour is not desirable. We are presenting a method for the dynamic adjustment of the weighting parameters, that is only depending on the underlying data and does not need any prior information. The method is especially apt to handle blurred, noisy, and deficient data, as it is often the case in biological microscopy.

Registration of point clouds is required in the processing of large biological data sets. The trade off between computation time and accuracy of the registration is the main challenge in this task. We present a novel method for registering point clouds in two and three dimensional space based on Group Averaging on the Euclidean transformation group. It is applied on a set of neighboring points whose size directly controls computing time and accuracy. The method is evaluated regarding dependencies of the computing time and the registration accuracy versus the point density assuming their random distribution. Results are verified in two biological applications on 2D and 3D images.

In this paper, we present a novel approach for a trainable rotation invariant detection of complex structures in 3D microscopic multichannel data using a nonlinear filter approach. The basic idea of our approach is to compute local features in a window around each 3D position and map these features by means of a nonlinear mapping onto new local harmonic descriptors of the local window. These local harmonic descriptors are then combined in a linear way to form the output of the filter. The optimal combination of the computed local harmonic descriptors is determined in previous training step, and allows the filter to be adapted to an arbitrary structure depending on the problem at hand. Our approach is not limited to scalar-valued images and can also be used for vector-valued (multichannel) images such as gradient vector flow fields. We present realizations of a scalar-valued and a vector-valued multichannel filter. Our proposed algorithm was quantitatively evaluated on colorectal cancer cell lines (cells grown under controlled conditions), on which we successfully detected complex 3D mitotic structures. For a qualitative evaluation we tested our algorithms on human 3D tissue samples of colorectal cancer. We compare our results with a steerable filter approach as well as a morphology-based approach.

In this paper, we present a novel approach for identifying objects using touch sensors installed in the finger tips of a manipulation robot. Our approach operates on low-resolution intensity images that are obtained when the robot grasps an object. We apply a bag-of-words approach for object identification. By means of unsupervised clustering on training data, our approach learns a vocabulary from tactile observations which is used to generate a histogram codebook. The histogram codebook models distributions over the vocabulary and is the core identification mechanism. As the objects are larger than the sensor, the robot typically needs multiple grasp actions at different positions to uniquely identify an object. To reduce the number of required grasp actions, we apply a decision-theoretic framework that minimizes the entropy of the probabilistic belief about the type of the object. In our experiments carried out with various industrial and household objects, we demonstrate that our approach is able to discriminate between a large set of objects. We furthermore show that using our approach, a robot is able to distinguish visually similar objects that have different elasticity properties by using only the information from the touch sensor.

In this paper, polar and spherical Fourier analysis are defined as the decomposition of a function in terms of eigenfunctions of the Laplacian with the eigenfunctions being separable in the corresponding coordinates. The proposed transforms provide effective decompositions of an image into basic patterns with simple radial and angular structures. The theory is compactly presented with an emphasis on the analogy to the normal Fourier transform. The relation between the polar or spherical Fourier transform and the normal Fourier transform is explored. As examples of applications, rotation-invariant descriptors based on polar and spherical Fourier coefficients are tested on pattern classification problems.

We propose a watermarking scheme for color images based on local quaternion Fourier spectral analysis (LQFSA).The merits of the proposed scheme include: 1) Quaternion Fourier transform is defined in a 4D vector space and thus provides a larger embedding scope for watermark than conventional monochannel transformation techniques. 2) We improve the imperceptibility of watermark with regard to human color vision properties through LQFSA. 3) We introduce invariant feature transform (IFT) and geometric correction scheme so as to enhance the robustness to extensive attacks, which is another essential factor to evaluate a watermarking scheme. 4) We adopt the nearest-neighborhood search to ensure the correctness of watermark extraction. Extensive experiments on the Stirmark platform validate the aforementioned merits.

We present a novel method for the fast computation of rotation invariant ¿local binary patterns¿ (LBP) on 3D volume data. Unlike a previous publication on 3D LBP, this new approach is not limited to ¿uniform patterns¿, providing a real 3D extension of the standard and rotation invariant LBP. We evaluate our methods in the context of 3D texture analysis of biological data.

The calculation of local features at points of interest is a vital part of many current image retrieval and object detection systems. The wavelet-based interest point detector by Loupias et al. was especially developed for image retrieval applications. We show how the detector can be extended by a Laplacian scale selection mechanism to provide scale information and compare it to other state of the art detectors. The extended detector is very well suited for visual object class recognition using feature cluster histograms. It discovers a variety of image structures distributed over the entire image, and the number of regions obtained can be adjusted easily. These properties lead to superior performance, which we confirmed by tests on a difficult animal categorization problem.

Many current object class models build on visual parts that constitute an object. However, visually different entities may actually refer to the same object part. This may be harmful for part based object class models. We present a method how visually distinct parts with the same semantic role can be associated by creating groupings based on the similarity of their occurrence distributions. Experimental results verify that more compact class representations can be built based on these groupings, which lead to improved classification performance and/or reduced classification time.

It is well known that linear filters are not powerful enough for many low-level image processing tasks. However, it is also very difficult to design robust nonlinear filters that respond exclusively to features of interest and that are, at the same time, equivariant with respect to translation and rotation. This paper proposes a new class of rotation-equivariant nonlinear filters that is based on the principle of group integration. These filters become efficiently computable by an iterative scheme based on repeated differentiation of products and summations of intermediate results. The relations of the proposed approach to Volterra filters and steerable filters are shown. In the context of detection problems, the filter may be interpreted as some kind of generalized Hough transform. The experiments show that the new filter can be used for enhancing noisy contours and rapid object detection in microscopical images. In the detection context, our experiments show that the proposed filter is definitely superior to alternative approaches, when high localization accuracy is required.

Steerable filters are a valuable tool for various low-level vision tasks. In this paper, we argue for the use of complex analysis in the context of 2-D steerable filters. In particular, we recommend the use of complex partial derivatives as a computational basis. Complex derivatives have a major advantage in comparison to real derivatives: they show a canonical rotation behavior, namely a rotation affects the derivative just by a multiplication with a complex unit number. So, the complex derivatives can be steered in a more elegant way and above that they are less expensive to compute. We present several analytical formulas for common and new filter kernels in terms of complex derivatives. Further we relate the complex derivatives of a Gaussian with the Gauss-Laguerre transform and show that the Gauss-Laguerre functions provide an optimal signal representation for local and smooth images. We discuss various finite difference schemes for the realization of the derivatives and use them in practice. In a first experiment, we use a newly introduced filter kernel for anisotropic blurring. The complex formalism offers an elegant way to locally adapt the shape and orientation of the kernel. Second, we use the proposed filters as matched filters to detect vessels in retinal images.

In this paper, we present a vision-based approach to mobile robot localization that integrates an image-retrieval system with Monte Carlo localization. The image-retrieval process is based on features that are invariant with respect to image translations and limited scale. Since it furthermore uses local features, the system is robust against distortion and occlusions, which is especially important in populated environments. To integrate this approach with the sample-based Monte Carlo localization technique, we extract for each image in the database a set of possible viewpoints using a two-dimensional map of the environment. Our technique has been implemented and tested extensively. We present practical experiments illustrating that our approach is able to globally localize a mobile robot, to reliably keep track of the robot's position, and to recover from localization failures. We furthermore present experiments designed to analyze the reliability and robustness of our approach with respect to larger errors in the odometry.

In this paper, we give a comprehensive description of our writer-independent online handwriting recognition system frog on hand. The focus of this work concerns the presentation of the classification/training approach, which we call cluster generative statistical dynamic time warping (CSDTW). CSDTW is a general, scalable, HMM-based method for variable-sized, sequential data that holistically combines cluster analysis and statistical sequence modeling. It can handle general classification problems that rely on this sequential type of data, e.g., speech recognition, genome processing, robotics, etc. Contrary to previous attempts, clustering and statistical sequence modeling are embedded in a single feature space and use a closely related distance measure. We show character recognition experiments of frog on hand using CSDTW on the UNIPEN online handwriting database. The recognition accuracy is significantly higher than reported results of other handwriting recognition systems. Finally, we describe the real-time implementation of frog on hand on a Linux Compaq iPAQ embedded device.

A technique to group contour points into line segments is presented in this paper. A Hough transform extended signature function with the angle parameter as a reference parameter is defined to reduce the contour grouping from 2D to 1D. An analysis shows that the signature function is piecewise linear with transition point corresponding to the turning points of a contour. Its stepwise derivative function is computed for the separation points in a set of contour points. With a changing angle as the reference parameter, we can vary the strength of the discontinuity of the signature function, to find almost all significant separation points. These points are further evaluated by three criteria (angle, piecewise error and total error) proposed later for the most representative separation points, between which the contour points are grouped together and are fitted into different line segments. Experiments with generated and real images are given to demonstrate the functionality of the algorithm.

We present a vision-based approach to mobile robot localization, that integrates an image retrieval system with Monte-Carlo localization. The image retrieval process is based on features that are invariant with respect to image translations, rotations, and limited scale. Using the local features the system is robust against distortion and occlusions, which is especially important in populated environments. By using the sample-based Monte-Carlo localization technique our robot is able to globally localize itself to reliably keep tracking of its position, and to recover from localization failures. Both techniques are combined by extracting for each image a set of possible view-points using a two-dimensional map of the environment. Our technique was implemented and tested extensively. We present several experiments demonstrating the reliability and robustness of our approach even in the context of dynamics in the environment and larger errors in the odometry.

We propose a novel similarity measure for hidden Markov models (HMMs). This measure calculates the Bayes probability of error for HMM state correspondences and propagates it along the Viterbi path in a similar way to the HMM Viterbi scoring. It can be applied as a tool to interpret misclassifications, as a stop criterion in iterative HMM training or as a distance measure for HMM clustering. The similarity measure is evaluated in the context of online handwriting recognition on lower case character models which have been trained from the UNIPEN database. We compare the similarities with experimental classifications. The results show that similar and misclassified class pairs are highly correlated. The measure is not limited to handwriting recognition, but can be used in other applications that use HMM based methods.

An algorithm to group edge points into digital line segments with Hough transformation is described. The edge points are mapped onto the parameter domain discretized at specific intervals, on which peaks appear to represent different line segments. By modeling each peak as a Gaussian function in the parameter domain, a region to which the edge points are supposed to be mapped is determined. Then the edge points are grouped and the parameters for a line segment are computed. For the edges including multiple line segments, a sequential Hough transformation for detecting peaks one by one in the parameter domain is implemented, and the points from the region around each peak are grouped, thus the line segments are described. Experiments show the robustness of the algorithm implemented on both the generated edges disturbed by different noise levels and real images taken from an indoor environment.

This paper presents a multilevel algorithm for straight line extraction and matching from stereo intensity images based on fuzzy strategies. The ultimate goal of our work is to find 3D landmarks represented in the form of straight lines. In this method line extracting not only uses the information of current level but also considers the lines extracted at the coarser level. The idea as similar to multi-scale edge focusing, except that a fuzzy evaluation procedure is carried out to control the quality of a line candidate. This paper also proposes a new matching strategy based on fuzzy-sets, where various matching constraints can be effectively combined and some matching information from the coarser level is also considered. This method needs only one-step matching and avoids inadequate overstrong constraints, so that reliable unique line matches can be achieved with a relatively small cost.

This paper presents an improved method for image thresholding by optimization of fuzzy compactness which was originally introduced by Pal-Rosenfeld (1988). In our method a set of asymmetric S-functions whose windows are located in the same range are used as membership functions for obtaining fuzzy compactness. This avoids the problem which may occur in the original algorithm by unsuitably choosing of window size. An effective algorithm for finding the optimum is developed which proved to be computationally faster. An application using this method to segment the regions of interesting of flame images is also demonstrated.

The method of Fourier descriptors is extended to produce a set of normalized coefficients which are invariant under any affine transformation (translation, rotation, scaling, and shearing). The method is based on a parameterized boundary description which is transformed to the Fourier domain and normalized there to eliminate dependencies on the affine transformation and on the starting point. Invariance to affine transforms allows considerable robustness when applied to images of objects which rotate in all three dimensions, as is demonstrated by processing silhouettes of aircraft maneuvering in three-space.>

The Viterbi algorithm is an efficient technique to estimate the state sequence of a discrete-time finite-state Markov process in the presence of memoryless noise. This work sets up a relationship to a general class of linear and nonlinear fast algorithms such as FFT, FWT, and optimal sorting. The performance of a Viterbi detector is a function of the minimum distance between signals in the observation space of the estimated Markov process. It is shown that this distance may efficiently be calculated with dynamic programming using a slightly modified Viterbi algorithm of an increased basis.