Any neuro-evolutionary algorithm that solves complex problems needs to deal with the issue of computational complexity. We show how a neural network (feed-forward, recurrent or RBF) can be transformed and then compiled in order to achieve fast execution speeds without requiring dedicated hardware like FPGAs. The compiled network uses a simple external data structure-a vector-for its parameters. This allows the weights of the neural network to be optimised by the evolutionary process without the need to re-compile the structure. In an experimental comparison our method effects a speedup of factor 5-10 compared to the standard method of evaluation (i.e., traversing a data structure with optimised C++ code).

This paper covers a fundamental problem of local phase based signal processing: the isotropic generalization of the classical 1D analytic signal to two dimensions. The well known analytic signal enables the analysis of local phase and amplitude information of 1D signals. Local phase, amplitude and additional orientation information can be extracted by the 2D monogenic signal with the restriction to the subclass of intrinsically one dimensional signals. In case of 2D image signals the monogenic signal enables the rotationally invariant analysis of lines and edges. In this work we present the 2D analytic signal as a novel generalization of both the analytic signal and the 2D monogenic signal. In case of 2D image signals the 2D analytic signal enables the isotropic analysis of lines, edges, corners and junctions in one unified framework. Furthermore, we show that 2D signals exist per se in a 3D projective subspace of the homogeneous conformal space which delivers a descriptive geometric interpretation of signals providing new insights on the relation of geometry and 2D signals.

In this article a new method is presented to obtain a full and precise calibration of camera-robot systems with eye-in-hand cameras. It achieves a simultaneous and numerically stable calibration of intrinsic and extrinsic camera parameters by analysing the image coordinates of a single point marker placed in the environment of the robot. The method works by first determining a rough initial estimate of the camera pose in the tool coordinate frame. This estimate is then used to generate a set of uniformly distributed calibration poses from which the object is visible. The measurements obtained in these poses are then used to obtain the exact parameters with CMA-ES (Covariance Matrix Adaptation Evolution Strategy), a derandomised variant of an evolution strategy optimiser. Minimal claims on the surrounding area and flexible handling of environmental and kinematical limitations make this method applicable to a range of robot setups and camera models. The algorithm runs autonomously without supervision and does not need manual adjustments. Our problem formulation is directly in the 3D space which helps in minimising the resulting calibration errors in the robot's task space. Both simulations and experimental results with a real robot show a very good convergence and high repeatability of calibration results without requiring user-supplied initial estimates of the calibration parameters.

In this article we present a new method for the pruning of unnecessary connections from neural networks created by an evolutionary algorithm (neuro-evolution). Pruning not only decreases the complexity of the network but also improves the numerical stability of the parameter optimisation process. We show results from experiments where connection pruning is incorporated into EANT2, an evolutionary reinforcement learning algorithm for both the topology and parameters of neural networks. By analysing data from the evolutionary optimisation process that determines the network's parameters, candidate connections for removal are identified without the need for extensive additional calculations.

In this article we present results from experiments where a edge detector was learned from scratch by EANT2, a method for evolutionary reinforcement learning. The detector is constructed as a neural network that takes as input the pixel values from a given image region-the same way that standard edge detectors do. However, it does not have any per-image parameters. A comparison between the evolved neural networks and two standard algorithms, the Sobel and Canny edge detectors, shows very good results.

This article presents results from experiments where a detector for defects in visual inspection images was learned from scratch by EANT2, a method for evolutionary reinforcement learning. The detector is constructed as a neural network that takes as input statistical data on filter responses from a bank of image filters applied to an image region. Training is done on example images with weakly labelled defects. Experiments show good results of EANT2 in an application area where evolutionary methods are rare.

In this paper we present a Common Genetic Encoding (CGE) for networks that can be applied to both direct and indirect encoding methods. As a direct encoding method, CGE allows the implicit evaluation of an encoded phenotype without the need to decode the phenotype from the genotype. On the other hand, one can easily decode the structure of a phenotype network, since its topology is implicitly encoded in the genotype's gene-order. Furthermore, we illustrate how CGE can be used for the indirect encoding of networks. CGE has useful properties that makes it suitable for evolving neural networks. A formal definition of the encoding is given, and some of the important properties of the encoding are proven such as its closure under mutation operators, its completeness in representing any phenotype network, and the existence of an algorithm that can evaluate any given phenotype without running into an infinite loop.

We propose two new developments for our supervised local linear approximation technique, the so called Hierarchical Network of Locally Arranged Models. A new model will be presented that defines those local regions of the input space in which linear models are trained to approximate the target function. This model is based on a one-class support vector machine and helps to improve the approximation quality. Secondly, an online learning algorithm for our approach will be described that can be used in applications where training data is only available as a continuous stream of samples. It allows to adapted a network to a function that may change over time. The success of these two developments is proven with three benchmark tests.

We propose an ensemble technique to train multiple individual models for supervised learning tasks. The new method divides the input space into local regions which are modelled as a set of hyper-ellipsoids. For each local region an individual model is trained to approximate or classify data efficiently. The idea is to use locality in the input space as an useful constraint to realize diversity in an ensemble. The method automatically determines the size of the ensemble, realises an outlier detection mechanism and shows superiority over comparable methods in a benchmark test. Also, the method was extended to a hierarchical framework allowing a user to solve complex learning tasks by combining different sub-solutions and information sources.

In the energy spectrum of an occlusion sequence, the distortion term has the same orientation as the velocity of the occluding signal. Other works claimed that this oriented structure can be used to distinguish the occluding velocity from the occluded one. We argue that the orientation structure of the distortion cannot always work as a reliable feature due to the rapidly decreasing energy contribution. This already weak orientation structure is further blurred by a superposition of distinct distortion components. We also indicate that the superposition principle of Shizawa and Mase (1991) for multiple motion estimation needs to be adjusted.

In this paper we propose a new 3D kernel for the recovery of 3D-orientation signatures. The kernel is a Gaussian function defined in local spherical coordinates and its Cartesian support has the shape of a truncated cone with its axis in the radial direction and very small angular support. A set of such kernels is obtained by uniformly sampling the 2D space of polar and azimuth angles. The projection of a local neighborhood on such a kernel set produces a local 3D-orientation signature. In the case of spatiotemporal analysis, such a kernel set can be applied either on the derivative space of a local neighborhood or on the local Fourier transform. The well known planes arising from single or multiple motion produce maxima in the orientation signature. Due to the kernel's local support spatiotemporal signatures possess higher orientation resolution than 3D steerable filters and motion maxima can be detected and localized more accurately. We describe and show in experiments the superiority of the proposed kernels compared to Hough transformation or EM-based multiple motion detection.

Junctions are significant features in images with intensity variation that exhibits multiple orientations. This makes the detection and characterization of junctions a challenging problem. The characterization of junctions would ideally be given by the response of a filter at every orientation. This can be achieved by the principle of steerability that enables the decomposition of a filter into a linear combination of basis functions. However, current steerability approaches suffer from the consequences of the uncertainty principle: in order to achieve high resolution in orientation they need a large number of basis filters increasing, thus, the computational complexity. Furthermore, these functions have usually a wide support which only accentuates the computational burden. We propose a novel alternative to current steerability approaches. It is based on utilizing a set of polar separable filters with small support to sample orientation information. The orientation signature is then obtained by interpolating orientation samples using Gaussian functions with small support. Compared with current steerability techniques our approach achieves a higher orientation resolution with a lower complexity. In addition, we build a polar pyramid to characterize junctions of arbitrary inherent orientation scales.

In this article we want to introduce first the Gabor wavelet network as a model based approach for an effective and efficient object representation. The Gabor wavelet network has several advantages such as invariance to some degree with respect to translation, rotation and dilation. Furthermore, the use of Gabor filters ensured that geometrical and textural object features are encoded. The feasibility of the Gabor filters as a model for local object features ensures a considerable data reduction while at the same time allowing any desired precision of the object representation ranging from a sparse to a photo-realistic representation. In the second part of the paper we will present an approach for the estimation of a head pose that is based on the Gabor wavelet networks. 1 Introduction Recently, model-based approaches for the recognition and the interpretation of images of variable objects, like the bunch graph approach, PCA, eigenfaces and active appearance models, have re...

We present a method for visual face tracking that is based on a wavelet representation of a face template. The wavelet representation allows: arbitrary affine deformations of the facial image; generalization from an individual face template to a rather general face template; and adapting the computational needs of the tracking algorithm to the computational resources available. The method presented was implemented on a Linux Pentium 450 MHz and runs off-line with 25 Hz, and online using an active camera mount at 22 Hz. We present experimental results on the off-line tests on several common image sequences including the salesman-sequence as well as on the online tests.

We present a novel MLP-type neural network based on hyperbolic numbers $the hyperbolic multilayer perceptron (HMLP). The neurons of the HMLP compute 2D-hyperbolic orthogonal transformations as weight propagation functions. The HMLP can therefore be seen as the hyperbolic counterpart of the known complex MLP. The HMLP is proven to be a universal approximator. Furthermore, a suitable backpropagation algorithm for it is derived. It is shown by experiments that the HMLP can learn tasks with underlying hyperbolic properties much more accurately and efficiently than a complex MLP and an ordinary MLP.

The computation of optical flow is a well studied topic in biological and computational vision. However, the existence of multiple motions in dynamic imagery due to occlusion or even transparency still raises challenging questions. In this paper, we propose an approach for the detection and characterization of occlusion and transparency. We propose a theoretical framework for both types of multiple motions which explicitly shows the difference between occlusion and transparency in the frequency domain. Then, we employ an EM-algorithm for the computation of one or two image velocities and a simple test for the detection of occlusion. Our approach differs from other EM-approaches which blindly assume the superposition of two models in the spatial domain without providing with a separate formal model for occlusion. We test and compare the characterization performance on synthetic and real data.

The computational cost of conventional filter methods for junction characterization is very high. This burden can be attenuated by using steerable filters. However, in order to achieve a high orientational selectivity to characterize complex junctions a large number of basis filters is necessary. From this results a yet too high computational effort for steerable filters. In this paper we present a new method for characterizing junctions which keeps the high orientational resolution and is computationally efficient. It is based on applying rotated copies of a wedge averaging filter and estimating the derivative with respect to the polar angle. The new method is compared with the steerable wedge filter method in experiments with real images. We show the superiority of our method as well as its adaptability to scale changes and robustness against noise.

We introduce quaternionic Gabor filters for the classification of local image structure. These filters are constructed as windowed basis functions of the quaternionic Fourier transform. We show that-in contrast to the 2D complex Gabor filters-the quaternionic Gabor filters are intrinsically 2D filters. A generalized phase concept is introduced and compared to the classical one. It is shown how local image structure can be classified by the value of the local quaternionic phase.

We introduce a low-level image representation using local orientation on a steerable pyramid. Its performance is demonstrated for a progressive image coder which transmits and reconstructs parts of an image guided by their similarity to a given sample image. Similar to human visual attention, the image is scanned in the most-important-first order to gain a maximum of visual information with minimum code.

In the quest for machines that are able to learn, reinforcement learning (RL) is found to be an appealing learning methodology. A known problem in this learning method, however is that it takes too long before the robot learns to associate suitable situation-action pairs. Due to this problem, RL has remained applicable only to simple tasks and discrete environment. To accelerate the learning process to a level required by real robot tasks, the traditional learning architecture has to be modified. We propose a modified reinforcement based robot skill acquisition and adaptation architecture. The architecture has two components: a bias and a learning components. The bias component imparts to the learner coarse a priori knowledge about the task. Subsequently, the learner refines the acquired actions through reinforcement learning. We have validated the architecture and the learning algorithm on a simulated TRC mobile robot for a goal reaching task.

A tabula rasa learning technique has worked well in well defined grid like problems (Barto et al., 1993). Nevertheless, it has severe limitations when applied in complex domains. In order to build a true learning system in complex domains, we have to begin to integrate a considerable amount of bias with the learner that has the ability to adapt a priori knowledge. This bias can assume a variety of forms. In this paper, in addition to reflex rules (Millan, 1996), symbolic knowledge about the environment is embedded into the learning system (Kaelbling, 1993). The incorporation of such knowledge aids the learner to identify and split key states rapidly. The learner is tested on a B21 robot for a goal reaching task. Experimental results show that after few trials the robot has indeed learned to unfold its path and to consistently follow the shortest path to the goal.

The application of an elastic graph-matching approach to discriminate facial image regions is presented. In contrast to the dynamic link architecture introduced by the Malsburg group, our application is not an identification task but a classification task. Therefore, our approach differs in several important aspects: (1) the choice of the filter set, (2) the selection of the positions of the nodes of the graph to represent the characteristic image information, (3) the generation of a representative reference pattern needed for the calculation of the classifications, and (4) a new two-step graph-matching approach based on the simulated annealing technique. The approach was tested on facial regions taking the eye region as an example target. A classification performance for the verification of eye regions of more than 93% was achieved.

A new method for analyzing the intrinsic dimensionality (ID) of low-dimensional manifolds in high-dimensional feature spaces is presented. Compared to a previous approach by Fukunaga and Olsen (1971), the method has only linear instead of cubic time complexity with respect to the dimensionality of the input space. Moreover, it is less sensitive to noise than the former approach. Experiments include ID estimation of synthetic data for comparison and illustration as well as ID estimation of an image sequence.

Usually, the first processing step in computer vision systems consists of a spatial convolution with only a few simple filters. Therefore, information is lost of it is not represented explicitly for the following processing steps. This paper proposes a new hierarchical filter scheme that can efficiently synthesize the responses for a large number of specific filters. The scheme is based on steerable filters. It also allows for an efficient on-line adjustment of the trade off between the speed and the accuracy of the filters. We apply this method to the detection of facial keypoints, especially the eye corners. These anatomically defined keypoints exhibit a large variability in their corresponding image structures so that a flexible low level feature extraction is required.

In this contribution Dynamic Cell Structures (DCS network) are applied to classify local image structures at particular facial landmarks. The facial landmarks such as the corners of the eyes or intersections of the iris with the eyelid are computed in advance by a combined model and data driven sequential search strategy. To reduce the detection error after the processing of the sequential search strategy, the computed image positions are verified applying a DCS network. The DCS network is trained by supervised learning with feature vectors which encode spatially arranged edge and structural information at the keypoint position considered. The model driven localization as well as the data driven verification are based on steerable filters, which build a representation comparable with one provided by a receptive field in the human visual system. We apply a DCS based classifier because of its ability to grasp the topological structure of complex input spaces and because it has proved successful in a number of other classification tasks. In our experiments the average error resulting from false positive classifications is less than 1%.

The authors introduce a method for the automatic detection of facial features and characteristic anatomical keypoints. In the application they are aiming at the anatomical landmarks are used to accurately measure facial features. Their approach is essentially bused on a selective search and sequential tracking of characteristic edge and line structures of the facial object to be searched. It integrates model knowledge to guarantee a consistent interpretation of the abundance of local features. The search and the tracking is controlled in each step by interpreting the already derived edge and line information in the context of the whole considered region. For their application, the edge and line detection has to be very precise and flexible. Therefore, they apply a powerful filtering scheme based on steerable filters.

We present geometric algebra as a new framework for the theory and computation of invariants and multiple-view constraints in computer vision. We discuss the formation of 3D projective invariants and a wholly geometric formulation of constraints from a number of images.

This paper presents a new self-organizing type RBF neural network and introduces the geometric algebra framework in the neurocomputing field. Real valued neural nets for function approximation require feature enhancement, dilation and rotation operations and are limited by the Euclidean metric. The authors believe that more general and flexible neural networks should be designed in order to capture important geometric characteristics of the manifolds. This is an important goal overlooked ever since. Geometric algebra is a system which allows the design of neural networks in a coordinate-free frame work to process patterns between layers using different dimensions and desired metric. The potential of such nets working in a Clifford algebra C(V/sub p,q/) is shown by a simple application of frame coordination in robotics.

We present geometric algebra as system for analysing the geometry of multiple-view images. The power of this approach is illustrated by giving purely geometric derivations of the constraints, for point and line correspondences in n-views and via a discussion of projective structure.

We address a way of depth estimation using the mechanical degrees of freedom of a stereo vision system. We apply a phase-based approach to compute disparity maps on different resolution, in an action-perception cycle. First, a gaze controller fixates the selected gaze points of the image. Then the vergence movement is commanded. The depth is computed by triangulation after convergence. This strategy (gaze and vergence control) overcomes the problem of large disparities and allows the computation of absolute depth in real time (25 Hz).

Facial keypoints such as eye corners are important features for a number of different tasks in automatic face processing. The problem is that facial keypoints rather have an anatomical high-level definition than a low-level one. Therefore, they cannot be detected reliably by purely data-driven methods like corner detectors that are only based on the image data of the local neighborhood. In this contribution we introduce a method for the automatic detection of facial keypoints. The method integrates model knowledge to guarantee a consistent interpretation of the abundance of local features. The detection is based on a selective search and sequential tracking of edges controlled by model knowledge. For this, the edge detection has to be very flexible. Therefore, we apply a powerful filtering scheme based on steerable filters.

We present geometric algebra, as a new, framework for the theory and computation of invariants in computer vision and compare it with the currently popular Grassmann-Cayley algebra. We also discuss the formation, of 3D projective invariants in terms of image coordinates.

Dynamic cell structures (DCS) represent a family of artificial neural architectures suited both for unsupervised and supervised learning. They belong to the recently (Martinetz 1994) introduced class of topology representing networks (TRN) that build perfectly topology preserving feature maps. DCS employ a modified Kohonen learning rule in conjunction with competitive Hebbian learning. The Kohonen type learning rule serves to adjust the synaptic weight vectors while Hebbian learning establishes a dynamic lateral connection structure between the units reflecting the topology of the feature manifold. In case of supervised learning, i.e., function approximation, each neural unit implements a radial basis function, and an additional layer of linear output units adjusts according to a delta-rule. DCS is the first RBF-based approximation scheme attempting to concurrently learn and utilize a perfectly topology preserving map for improved performance. Simulations on a selection of CMU-Benchmarks indicate that the DCS idea applied to the growing cell structure algorithm (Fritzke 1993c) leads to an efficient and elegant algorithm that can beat conventional models on similar tasks.

Dynamic Cell Structures (DCS) represent a family of artificial neural architectures suited both for unsupervised and supervised learning. They belong to the recently [Martinetz94] introduced class of Topology Representing Networks (TRN) which build perlectly topology pre(cid:173) serving feature maps. DCS empI'oy a modified Kohonen learning rule in conjunction with competitive Hebbian learning. The Kohonen type learning rule serves to adjust the synaptic weight vectors while Hebbian learning establishes a dynamic lateral connection structure between the units reflecting the topology of the feature manifold. In case of super(cid:173) vised learning, i.e. function approximation, each neural unit implements a Radial Basis Function, and an additional layer of linear output units adjusts according to a delta-rule. DCS is the first RBF-based approxima(cid:173) tion scheme attempting to concurrently learn and utilize a perfectly to(cid:173) pology preserving map for improved performance. Simulations on a selection of CMU-Benchmarks indicate that the DCS idea applied to the Growing Cell Structure algorithm [Fritzke93] leads to an efficient and elegant algorithm that can beat conventional models on similar tasks.