In this paper, we introduce a novel framework for low-level image processing and analysis. First, we process images with very simple, difference-based filter functions. Second, we fit the 2-parameter Weibull distribution to the filtered output. This maps each image to the 2D Weibull manifold. Third, we exploit the information geometry of this manifold and solve low-level image processing tasks as minimisation problems on point sets. For a proof-of-concept example, we examine the image autofocusing task. We propose appropriate cost functions together with a simple implicitly-constrained manifold optimisation algorithm and show that our framework compares very favourably against common autofocus methods from literature. In particular, our approach exhibits the best overall performance in terms of combined speed and accuracy

We propose a novel method for iterative learning of point correspondences between image sequences. Points moving on surfaces in 3D space are projected into two images. Given a point in either view, the considered problem is to determine the corresponding location in the other view. The geometry and distortions of the projections are unknown as is the shape of the surface. Given several pairs of point-sets but no access to the 3D scene, correspondence mappings can be found by excessive global optimization or by the fundamental matrix if a perspective projective model is assumed. However, an iterative solution on sequences of point-set pairs with general imaging geometry is preferable. We derive such a method that optimizes the mapping based on Neyman's chi-square divergence between the densities representing the uncertainties of the estimated and the actual locations. The densities are represented as channel vectors computed with a basis function approach. The mapping between these vectors is updated with each new pair of images such that fast convergence and high accuracy are achieved. The resulting algorithm runs in real-time and is superior to state-of-the-art methods in terms of convergence and accuracy in a number of experiments.

In this paper, we present a novel scheme for anisotropic diffusion driven by the image autocorrelation function. We show the equivalence of this scheme to a special case of iterated adaptive filtering. By determining the diffusion tensor field from an autocorrelation estimate, we obtain an evolution equation that is computed from a scalar product of diffusion tensor and the image Hessian. We propose further a set of filters to approximate the Hessian on a minimized spatial support. On standard benchmarks, the resulting method performs favorable in many cases, in particular at low noise levels. In a GPU implementation, video real-time performance is easily achieved.

Channel-coded feature maps (CCFMs) represent arbitrary image features using multi-dimensional histograms with soft and overlapping bins. This representation can be seen as a generalization of the SIFT descriptor, where one advantage is that it is better suited for computing derivatives with respect to image transformations. Using these derivatives, a local optimization of image scale, rotation and position relative to a reference view can be computed. If piecewise polynomial bin functions are used, e.g. B-splines, these histograms can be computed by first encoding the data set into a histogram-like representation with non-overlapping multi-dimensional monomials as bin functions. This representation can then be processed using multi-dimensional convolutions to obtain the desired representation. This allows to reuse much of the computations for the derivatives. By comparing the complexity of this method to direct encoding, it is found that the piecewise method is preferable for large images and smaller patches with few channels, which makes it useful, e.g. in early steps of coarse-to-fine approaches.

Intrinsic dimensionality is a concept introduced by statistics and later used in image processing to measure the dimensionality of a data set. In this paper, we introduce a continuous representation of the intrinsic dimension of an image patch in terms of its local spectrum or, equivalently, its gradient field. By making use of a cone structure and barycentric co-ordinates, we can associate three confidences to the three different ideal cases of intrinsic dimensions corresponding to homogeneous image patches, edge-like structures and junctions. The main novelty of our approach is the representation of confidences as prior probabilities which can be used within a probabilistic framework. To show the potential of our continuous representation, we highlight applications in various contexts such as image structure classification, feature detection and localisation, visual scene statistics and optic flow evaluation.

In this paper we present a novel method to implement the monogenic scale space on a rectangular domain. The monogenic scale space is a vector valued scale space based on the Poisson scale space, which establishes a sophisticated alternative to the Gaussian scale space. Previous implementations of the monogenic scale space are Fourier transform based, and therefore suffer from the implicit periodicity in case of finite domains. The features of the monogenic scale space, including local amplitude, local phase, local orientation, local frequency, and phase congruency, are much easier to interpret in terms of image features evolving through scale than in the Gaussian case. Furthermore, applying results from harmonic analysis, relations between the features are obtained which improve the understanding of image analysis. As applications, we present a very simple but still accurate approach to image reconstruction from local amplitude and local phase and a method for extracting the evolution of lines and edges through scale.

In this paper we address the topics of scale-space and phase-based image processing in a unifying framework. In contrast to the common opinion, the Gaussian kernel is not the unique choice for a linear scale-space. Instead, we chose the Poisson kernel since it is closely related to the monogenic signal, a 2D generalization of the analytic signal, where the Riesz transform replaces the Hilbert transform. The Riesz transform itself yields the flux of the Poisson scale-space and the combination of flux and scale-space, the monogenic scale-space, provides the local features phase-vector and attenuation in scale-space. Under certain assumptions, the latter two again form a monogenic scale-space which gives deeper insight to low-level image processing. In particular, we discuss edge detection by a new approach to phase congruency and its relation to amplitude based methods, reconstruction from local amplitude and local phase, and the evaluation of the local frequency.

This review article gives an overview on adaptive filtering methods based on channel representations. The framework of channel representations and its relation to density estimation is introduced. The fast and accurate scheme of virtual shift decoding is introduced and applied in several variants of channel smoothing:

•  channel smoothing with alpha-synthesis for improving stability of edge-enhancing filtering

•  orientation adaptive channel smoothing with applications to coherence-enhancing filtering

•  channel smoothing using graph-cuts for improving filtering results at corners

•  channel-coded feature maps (CCFMs) which lead to a significant speed-up of channel averaging

•  CCFM-based smoothing based on optimal parameters derived from a novel uncertainty relation

For each method, an algorithmic description and some examples of results are provided, together with discussions and references of the original papers. Cross connections to other articles in this volume are given where appropriate.

Feature hierarchies are essential to many visual object recognition systems and are well motivated by observations in biological systems. The present paper proposes an algorithm to incrementally compute feature hierarchies. The features are represented as estimated densities, using a variant of local soft histograms. The kernel functions used for this estimation in conjunction with their unitary extension establish a tight frame and results from framelet theory apply. Traversing the feature hierarchy requires resampling of the spatial and the feature bins. For the resampling, we derive a multi-resolution scheme for quadratic spline kernels and we derive an optimization algorithm for the upsampling. We complement the theoretic results by some illustrative experiments, consideration of convergence rate and computational efficiency.

In this paper we present a novel numerical approximation scheme for anisotropic diffusion which is at the same time a special case of iterated adaptive filtering. By assuming a sufficiently smooth diffusion tensor field, we simplify the divergence term and obtain an evolution equation that is computed from a scalar product of diffusion tensor and the Hessian. We propose further a set of filters to approximate the Hessian on a minimized spatial support. On standard benchmarks, the resulting method performs in average nearly as good as the best known denoising methods from the literature, although it is significantly faster and easier to implement. In a GPU implementation video real-time performance is achieved for moderate noise levels.

The estimation of a patch position in an image is a long established but still relevant topic with many applications, e.g. pose estimation and tracking in image sequences. In most systems the position estimate needs to be fused with other estimates, and hence, covariance information is required to weight the different estimates in the right way. In this paper we address the issue with covariance estimation in the case of sum of absolute difference (SAD) block matching. First, we derive the theory for covariance estimation in the case of SAD matching. Second, we evaluate the suggested method in a virtual 3D patch tracking scenario in order to verify the performance in real-world scenarios.

The assessment of image denoising results depends on the respective application area, i.e. image compression, still-image acquisition, and medical images require entirely different behavior of the applied denoising method. In this paper we propose a novel, nonlinear diffusion scheme that is derived from a linear diffusion process in a value space determined by the application. We show that application-driven linear diffusion in the transformed space compares favorably with existing nonlinear diffusion techniques. 

A method for online global pose estimation of aerial images by alignment with a georeferenced 3D model is presented.Motion stereo is used to reconstruct a dense local height patch from an image pair. The global pose is inferred from the 3D transform between the local height patch and the model.For efficiency, the sought 3D similarity transform is found by least-squares minimizations of three 2D subproblems.The method does not require any landmarks or reference points in the 3D model, but an approximate initialization of the global pose, in our case provided by onboard navigation sensors, is assumed.Real aerial images from helicopter and aircraft flights are used to evaluate the method. The results show that the accuracy of the position and orientation estimates is significantly improved compared to the initialization and our method is more robust than competing methods on similar datasets.The proposed matching error computed between the transformed patch and the map clearly indicates whether a reliable pose estimate has been obtained.

This paper presents an autonomous robotic system thatincorporates novel Computer Vision, Machine Learningand Data Mining algorithms in order to learn to navigateand discover important visual entities. This is achievedwithin a Learning from Demonstration (LfD) framework,where policies are derived from example state-to-actionmappings. For autonomous navigation, a mapping is learntfrom holistic image features (GIST) onto control parametersusing Random Forest regression. Additionally, visual entities(road signs e.g. STOP sign) that are strongly associatedto autonomously discovered modes of action (e.g. stoppingbehaviour) are discovered through a novel Percept-ActionMining methodology. The resulting sign detector is learntwithout any supervision (no image labeling or boundingbox annotations are used). The complete system is demonstratedon a fully autonomous robotic platform, featuring asingle camera mounted on a standard remote control car.The robot carries a PC laptop, that performs all the processingon board and in real-time.

This paper introduces a bundle adjustment (BA) method that obtains accurate structure and motion from rolling shutter (RS) video sequences: RSBA. When a classical BA algorithm processes a rolling shutter video, the resultant camera trajectory is brittle, and complete failures are not uncommon. We exploit the temporal continuity of the camera motion to define residuals of image point trajectories with respect to the camera trajectory. We compare the camera trajectories from RSBA to those from classical BA, and from classical BA on rectified videos. The comparisons are done on real video sequences from an iPhone 4, with ground truth obtained from a global shutter camera, rigidly mounted to the iPhone 4. Compared to classical BA, the rolling shutter model requires just six extra parameters. It also degrades the sparsity of the system Jacobian slightly, but as we demonstrate, the increase in computation time is moderate. Decisive advantages are that RSBA succeeds in cases where competing methods diverge, and consistently produces more accurate results.

Segmentation is an important preprocessing step in many applications. Purely colour-based segmentation is often problematic. For this reason, we here investigate fusion of depth and colour information, to facilitate robust segmentation of single images. We evaluate segmentation results on data collected using the Microsoft Kinect peripheral for Xbox 360, using superparamagnetic clustering. We also propose a method for aligning and encoding colour and depth information from the Kinect device. As we show in the paper, the fusion of depth and colour information produces more semantically relevant segments for scene analysis than either depth or colour separately.

A new approach to track bicycles from imagery sensor data is proposed. It is based on detecting ellipsoids in the images, and treat these pair-wise using a dynamic bicycle model. One important application area is in automotive collision avoidance systems, where no dedicated systems for bicyclists yet exist and where very few theoretical studies have been published.

Possible conflicts can be predicted from the position and velocity state in the model, but also from the steering wheel articulation and roll angle that indicate yaw changes before the velocity vector changes. An algorithm is proposed which consists of an ellipsoid detection and estimation algorithm and a particle filter.

A simulation study of three critical single target scenarios is presented, and the algorithm is shown to produce excellent state estimates. An experiment using a stationary camera and the particle filter for state estimation is performed and has shown encouraging results.

Techniques from the theory of partial differential equations are often used to design filter methods that are locally adapted to the image structure. These techniques are usually used in the investigation of gray-value images. The extension to color images is non-trivial, where the choice of an appropriate color space is crucial. The RGB color space is often used although it is known that the space of human color perception is best described in terms of non-euclidean geometry, which is fundamentally different from the structure of the RGB space. Instead of the standard RGB space, we use a simple color transformation based on the theory of finite groups. It is shown that this transformation reduces the color artifacts originating from the diffusion processes on RGB images. The developed algorithm is evaluated on a set of real-world images, and it is shown that our approach exhibits fewer color artifacts compared to state-of-the-art techniques. Also, our approach preserves details in the image for a larger number of iterations.

A common computer vision task is navigation and mapping. Many indoor navigation tasks require depth knowledge of at, unstructured surfaces (walls, oor, ceiling). With passive illumination only, this is an ill-posed problem. Inspired by small children using a torchlight, we use a spotlight for active illumination. Using our torchlight approach, depth and orientation estimation of unstructured, at surfaces boils down to estimation of ellipse parameters. The extraction of ellipses is very robust and requires little computational effort.

In this position paper, we seek to extend the layered perception-action paradigm for on-line learning such that it includes an explicit symbolic processing capability. By incorporating symbolic processing at the apex of the perception action hierarchy in this way, we ensure that abstract symbol manipulation is fully grounded, without the necessity of specifying an explicit representational framework. In order to carry out this novel interfacing between symbolic and sub-symbolic processing, it is necessary to embed fuzzy rst-order logic theorem proving within a variational framework. The online learning resulting from the corresponding Euler-Lagrange equations establishes an extended adaptability compared to the standard subsumption architecture. We discuss an application of this approach within the eld of advanced driver assistance systems, demonstrating that a closed-form solution to the Euler Lagrange optimization problem is obtainable for simple cases.

Linear scale-space theory is the fundamental building block for many approaches to image processing like pyramids or scale-selection. However, linear smoothing does not preserve image structures very well and thus non-linear techniques are mostly applied for image enhancement. A different perspective is given in the framework of channel-smoothing, where the feature domain is not considered as a linear space, but it is decomposed into local basis functions. One major drawback is the larger memory requirement for this type of representation, which is avoided if the channel representation is subsampled in the spatial domain. This general type of feature representation is called channel-coded feature map (CCFM) in the literature and a special case using linear channels is the SIFT descriptor. For computing CCFMs the spatial resolution and the feature resolution need to be selected.

In this paper, we focus on the spatio-featural scale-space from a scale-selection perspective. We propose a coupled scheme for selecting the spatial and the featural scales. The scheme is based on an analysis of lower bounds for the product of uncertainties, which is summarized in a theorem about a spatio-featural uncertainty relation. As a practical application of the derived theory, we reconstruct images from CCFMs with resolutions according to our theory. The results are very similar to the results of non-linear evolution schemes, but our algorithm has the fundamental advantage of being non-iterative. Any level of smoothing can be achieved with about the same computational effort.

This paper describes a system for structure-and-motion estimation for real-time navigation and obstacle avoidance. We demonstrate it technique to increase the efficiency of the 5-point solution to the relative pose problem. This is achieved by a novel sampling scheme, where We add a distance constraint on the sampled points inside the RANSAC loop. before calculating the 5-point solution. Our setup uses the KLT tracker to establish point correspondences across tone in live video We also demonstrate how an early outlier rejection in the tracker improves performance in scenes with plenty of occlusions. This outlier rejection scheme is well Slated to implementation on graphics hardware. We evaluate the proposed algorithms using real camera sequences with fine-tuned bundle adjusted data as ground truth. To strenghten oar results we also evaluate using sequences generated by a state-of-the-art rendering software. On average we are able to reduce the number of RANSAC iterations by half and thereby double the speed.

One major goal of the COSPAL project is to develop an artificial cognitive system architecture with the capability of exploratory learning. Exploratory learning is a strategy that allows to apply generalization on a conceptual level, resulting in an extension of competences. Whereas classical learning methods aim at best possible generalization, i.e., concluding from a number of samples of a problem class to the problem class itself, exploration aims at applying acquired competences to a new problem class. Incremental or online learning is an inherent requirement to perform exploratory learning.

Exploratory learning requires new theoretic tools and new algorithms. In the COSPAL project, we mainly investigate reinforcement-type learning methods for exploratory learning and in this paper we focus on its algorithmic aspect. Learning is performed in terms of four nested loops, where the outermost loop reflects the user-reinforcement-feedback loop, the intermediate two loops switch between different solution modes at symbolic respectively sub-symbolic level, and the innermost loop performs the acquired competences in terms of perception-action cycles. We present a system diagram which explains this process in more detail.

We discuss the learning strategy in terms of learning scenarios provided by the user. This interaction between user ('teacher') and system is a major difference to most existing systems where the system designer places his world model into the system. We believe that this is the key to extendable robust system behavior and successful interaction of humans and artificial cognitive systems.

We furthermore address the issue of bootstrapping the system, and, in particular, the visual recognition module. We give some more in-depth details about our recognition method and how feedback from higher levels is implemented. The described system is however work in progress and no final results are available yet. The available preliminary results that we have achieved so far, clearly point towards a successful proof of the architecture concept.

This paper explores the possibility to use a single low-resolution FIR camera for detection of pedestrians in the near zone in front of a vehicle. A low resolution sensor reduces the cost of the system, as well as the amount of data that needs to be processed in each frame.

We present a system that makes use of hot-spots and image positions of a near constant bearing to detect potential pedestrians. These detections provide seeds for an energy minimization algorithm that fits a pedestrian model to the detection. Since false alarms are hard to tolerate, the pedestrian model is then tracked, and the distance-to-collision (DTC) is measured by integrating size change measurements at sub-pixel accuracy, and the car velocity. The system should only engage braking for detections on a collision course, with a reliably measured DTC.

Preliminary experiments on a number of recorded near collision sequences indicate that our method may be useful for ranges up to about 10m using an 80x60 sensor, and somewhat more using a 160x120 sensor. We also analyze the robustness of the evaluated algorithm with respect to dead pixels, a potential problem for low-resolution sensors.

In this paper we propose a new approach to real-time view-based object recognition and scene registration. Object recognition is an important sub-task in many applications, as e.g., robotics, retrieval, and surveillance. Scene registration is particularly useful for identifying camera views in databases or video sequences. All of these applications require a fast recognition process and the possibility to extend the database with new material, i.e., to update the recognition system online. The method that we propose is based on P-channels, a special kind of information representation which combines advantages of histograms and local linear models. Our approach is motivated by its similarity to information representation in biological systems but its main advantage is its robustness against common distortions as clutter and occlusion. The recognition algorithm extracts a number of basic, intensity invariant image features, encodes them into P-channels, and compares the query P-channels to a set of prototype P-channels in a database. The algorithm is applied in a cross-validation experiment on the COIL database, resulting in nearly ideal ROC curves. Furthermore, results from scene registration with a fish-eye camera are presented.

Traditionally, quadrature filters and derivatives have been considered as alternative approaches to low-level image analysis. In this paper we show that there actually exist close connections: We define the quadrature-based boundary tensor and the derivative-based gradient energy tenser which exhibit very similar behavior. We analyse the reason for this and determine how to minimize the difference. These insights lead to a simple and very efficient integrated feature detection algorithm.

In this paper we briefly review a not so well known quadratic, phase invariant image processing operator, the energy operator, and describe its tensor-valued generalization, the energy tensor. We present relations to the real-valued and the complex valued energy operators and discuss properties of the three operators. We then focus on the discrete implementation for estimating the tensor based on Teager's algorithm and frame theory. The kernels of the real-valued and the tensor-valued operators are formally derived. In a simple experiment we compare the energy tensor to other operators for orientation estimation. The paper is concluded with a short outlook to future work.

 In this paper we discuss the benefits of writing code for a specific processor and exploiting all its capabilities. We shows that in some situations it is possible to significantly reduce the time consumption by using SSE2, a Single Instruction Multiple Data (SIMD) extension available in new Pentium processors. Speed of the Harris operator is used for evaluation. All experiments are run on a Pentium 4 and the results are compared between ordinary C-code and code using SSE2. The purpose is not only to achieve a significant speed-up of the code, but also to benefit from SSE2 code with the least possible programming effort.

The channel representation allows the construction of soft histograms, where peaks can be detected with a much higher accuracy than in regular hard-binned histograms. This is critical in e.g. reducing the number of bins of generalized Hough transform methods. When applying the maximum entropy method to the channel representation, a minimum-information reconstruction of the underlying continuous probability distribution is obtained. The maximum entropy reconstruction is compared to simpler linear methods in some simulated situations. Experimental results show that mode estimation of the maximum entropy reconstruction outperforms the linear methods in terms of quantization error and discrimination threshold. Finding the maximum entropy reconstruction is however computationally more expensive.

In this paper we address one of the standard problems of image processing and computer vision: The detection of points of interest (POI). We propose two new approaches for improving the detection results. First, we define an energy tensor which can be considered as a phase invariant extension of the structure tensor. Second, we use the channel representation for robustly clustering the POI information from the first step resulting in sub-pixel accuracy for the localisation of POI. We compare our method to several related approaches on a theoretical level and show a brief experimental comparison to the Harris detector.

In this paper we present a method to implement the monogenic scale space on a bounded domain and show some applications. The monogenic scale space is a vector valued scale space based on the Poisson scale space, which establishes a sophisticated alternative to the Gaussian scale space. The features of the monogenic scale space, including local amplitude, local phase, local orientation, local frequency, and phase congruency, are much easier to interpret in terms of image features evolving through scale than in the Gaussian case. Furthermore, applying results from harmonic analysis, relations between the features are obtained which improve the understanding of image analysis. As applications, we present a very simple but still accurate approach to image reconstruction from local amplitude and local phase and a method for extracting the evolution of lines and edges through scale.

Channel smoothing is an alternative to diffusion filtering for robust estimation of image features. Its main advantages are speed, stability with respect to parameter changes, and a simple implementation. However, channel smoothing becomes instable in certain situations, typically for elongated, periodic patterns like for instance fingerprints. As for the diffusion filtering an anisotropic extension is required in these cases. In this paper we introduce a new method for anisotropic channel smoothing which is comparable to coherence enhancing diffusion, but faster and easier to implement. Anisotropic channel smoothing implements an orientation adaptive non-linear filtering scheme as a special case of adaptive channel filtering. The smoothing algorithm is applied to several fingerprint images and the results are compared to those of coherence enhancing diffusion.

Disparity estimation is a fundamental problem of computer vision. Besides other approaches, disparity estimation from phase information is a quite wide-spread technique. In the present paper, we have considered the influence of the involved quadrature filters and we have replaced them with filters based on the monogenic signal. The implemented algorithm makes use of a scale-pyramid and applies channel encoding for the representation and fusion of the estimated data. The performed experiments show a significant improvement of the results.

We introduce a compact coding of image information which explicitely separates geometric information (orientation) and structural information (phase and color). We investigate the importance of these factors for stereo matching on a large data set. From these investigation we can conclude that it is their combination that gives the best results. Concrete weights for their relative importance are measured.

Augmented reality is a growing field, with many diverse applications ranging from TV and film production, to industrial maintenance, medicine, education, entertainment and games. The central idea is to add virtual objects into a real scene, either by displaying them in a see-through head-mounted display, or by superimposing them on an image of the scene captured by a camera. Depending on the application, the added objects might be virtual characters in a TV or film production, instructions for repairing a car engine, or a reconstruction of an archaeological site. For the effect to be believable, the virtual objects must appear rigidly fixed to the real world, which requires the accurate measurement in real-time of the position of the camera or the user-s head. Present technology cannot achieve this without resorting to systems that require a significant infrastructure in the operating environment, severely restricting the range of possible applications.

One major goal of the COSPAL project is to develop an artificial cognitive system architecture with the capability of exploratory learning. Exploratory learning is a strategy that allows to apply generalization on a conceptual level, resulting in an extension of competences. Whereas classical learning methods aim at best possible generalization, i.e., concluding from a number of samples of a problem class to the problem class itself, exploration aims at applying acquired competences to a new problem class. Incremental or online learning is an inherent requirement to perform exploratory learning.

Exploratory learning requires new theoretic tools and new algorithms. In the COSPAL project, we mainly investigate reinforcement-type learning methods for exploratory learning and in this paper we focus on its algorithmic aspect. Learning is performed in terms of four nested loops, where the outermost loop reflects the user-reinforcement-feedback loop, the intermediate two loops switch between different solution modes at symbolic respectively sub-symbolic level, and the innermost loop performs the acquired competences in terms of perception-action cycles. We present a system diagram which explains this process in more detail.

We discuss the learning strategy in terms of learning scenarios provided by the user. This interaction between user (’teacher’) and system is a major difference to most existing systems where the system designer places his world model into the system. We believe that this is the key to extendable robust system behavior and successful interaction of humans and artificial cognitive systems.

We furthermore address the issue of bootstrapping the system, and, in particular, the visual recognition module.We give some more in-depth details about our recognition method and how feedback from higher levels is implemented. The described system is however work in progress and no final results are available yet. The available preliminary results that we have achieved so far, clearly point towards a successful proof of the architecture concept.

In this paper we propose a new operator which combines advantages of monogenic scale-space and Gaussian scale-space, of the monogenic signal and the structure tensor. The gradient energy tensor (GET) defined in this paper is based on Gaussian derivatives up to third order using different scales. These filters are commonly available, separable, and have an optimal uncertainty. The response of this new operator can be used like the monogenic signal to estimate the local amplitude, the local phase, and the local orientation of an image, but it also allows to measure the coherence of image regions as in the case of the structure tensor

In this paper we present a new method to implement a robust estimator: B-spline channel smoothing. We show that linear smoothing of channels is equivalent to a robust estimator, where we make use of the channel representation based upon quadratic B-splines. The linear decoding from B-spline channels allows to derive a robust error norm which is very similar to Tukey's biweight error norm. Using channel smoothing instead of iterative robust estimator implementations like non-linear diffusion, bilateral filtering, and mean-shift approaches is advantageous since channel smoothing is faster, it is easy to implement, it chooses the global minimum error instead of the nearest local minimum, and it can also be used on non-linear spaces, such as orientation space. As an application, we implemented orientation smoothing and compared it to the other three approaches.

In this paper we address the problem of appropriately representing the intrinsic dimensionality of image neighborhoods. This dimensionality describes the degrees of freedom of a local image patch and it gives rise to some of the most often applied corner and edge detectors. It is common to categorize the intrinsic dimensionality (iD) to three distinct cases: i0D, i1D, and i2D. Real images however contain combinations of all three dimensionalities which has to be taken into account by a continuous representation. Based on considerations of the structure tensor, we derive a cone-shaped iD-space which leads to a probabilistic point of view to the estimation of intrinsic dimensionality.

In this paper we address the topics of scale-space and phase-based signal processing in a common framework. The involved linear scale-space is no longer based on the Gaussian kernel but on the Poisson kernel. The resulting scale-space representation is directly related to the monogenic signal, a 2D generalization of the analytic signal. Hence, the local phase arises as a natural concept in this framework which results in several advanced relationships that can be used in image processing.