Kristof Teelen

Fast polynomial segmentation of digitized curves

We propose a linear-time algorithm for curve segmentation which is based on constructive polynomial fitting This work extends previous work on constructive fitting by taking the topological properties of a digitized curve into account The algorithm uses uniform (or L∞) fitting and it works for segments of arbitrary thickness We illustrate the algorithm with the segmentation of contours into straight and parabolic segments.

Face Recognition Using Parabola Edge Map

Several applications such as access control, behaviour observation and videoconferencing require a real-time method for face recognition. We propose to represent faces with parabola segments with an algorithm that allows us to fit parabola segments real-time to edge pixels. Parabola offer a good description for the many edges in a face, which is advantageous for several applications such as recognition of the facial expression and facial orientation. We use parabola segments for face recognition, which is done by a technique that matches parabola segments from different faces, based on distance and intensity.

Vehicle Tracking Using Geometric Features

Applications such as traffic surveillance require a real-time and accurate method for object tracking. We propose to represent scene observations with parabola segments with an algorithm that allows us to fit parabola segments in real-time to edge pixels. The motion vectors for these parabola segments are obtained in consecutive frames by a matching technique based on distance and intensity. Furthermore, moving rigid objects are detected by an original method that clusters comparable motion vectors. The result is a robust detection and tracking method, which can cope with small changes in viewpoint on the moving rigid object.

Fire Detection in Color Images Using Markov Random Fields

Automatic video-based fire detection can greatly reduce fire alert delay in large industrial and commercial sites, at a minimal cost, by using the existing CCTV camera network. Most traditional computer vision methods for fire detection model the temporal dynamics of the flames, in conjunction with simple color filtering. An important drawback of these methods is that their performance degrades at lower framerates, and they cannot be applied to still images, limiting their applicability. Also, real-time operation often requires significant computational resources, which may be unfeasible for large camera networks. This paper presents a novel method for fire detection in static images, based on a Markov Random Field but with a novel potential function. The method detects 99.6% of fires in a large collection of test images, while generating less false positives then a state-of-the-art reference method. Additionally, parameters are easily trained on a 12-image training set with minimal user input.

Adaptive and optimal difference operators in image processing

Differential operators are essential in many image processing applications. Previous work has shown how to compute derivatives more accurately by examining the image locally, and by applying a difference operator which is optimal for each pixel neighborhood. The proposed technique avoids the explicit computation of fitting functions, and replaces the function fitting process by a function classification process using a filter bank of feature detection templates. Both the feature detectors and the optimal difference operators have a specific shape and an associated cost, defined by a rigid mathematical structure, which can be described by Grobner bases. This paper introduces a cost criterion to select the operator of the best approximating function class and the most appropriate template size so that the difference operator can be locally adapted to the digitized function. We describe how to obtain discrete approximates for commonly used differential operators, and illustrate how image processing applications can benefit from the adaptive selection procedure for the operators by means of two example applications: tangent computation for digitized object boundaries and the Laplacian of Gaussian edge detector.

Improving difference operators by local feature detection

Differential operators are required to compute several characteristics for continuous surfaces, as e.g tangents, curvature, flatness, shape descriptors We propose to replace differential operators by the combined action of sets of feature detectors and locally adapted difference operators A set of simple local feature detectors is used to find the fitting function which locally yields the best approximation for the digitized image surface For each class of fitting functions, we determine which difference operator locally yields the best result in comparison to the differential operator Both the set of feature detectors and the difference operator for a function class have a rigid mathematical structure, which can be described by Groebner bases In this paper we describe how to obtain discrete approximates for the Laplacian differential operator and how these difference operators improve the performance of the Laplacian of Gaussian edge detector.

Consensus sets for affine transformation uncertainty polytopes

We introduce an uncertainty model for geometric transformations that can be used in computer vision as well as interactive computer graphics. The model is based on polygonal uncertainty regions, transformation polytopes and their consensus sets. The most important result of this paper is that the RANSAC algorithm can be placed in a broader framework of search algorithms that look for good parameter uncertainty polytopes. To guide the search, each polytope has a consensus set whose size is a measure for its quality.

Computing the uncertainty of transformations in digital images

In this work we present the use and properties of a transformation uncertainty polytope for a frequently encountered problem in computer vision: registration in visual inspection. For each feature point in the reference image, a corresponding feature point must be distinguished in the test image among many candidates. A convex polytope is used to captivate the uncertainty of the transformation from the reference feature points to uncertainty regions in the test image in which the candidate matches are to be found. By checking the consistency of the uncertainty transformation for pairs of possible matches, we construct a consistency graph. The consistency graph gives us the necessary information to distinguish the good matches from the rest. Based on the best matches, we compute the registration transformation.

Adaptive Constructive Polynomial Fitting

To extract geometric primitives from edges, we use an incremental linear-time fitting algorithm, which is based on constructive polynomial fitting. In this work, we propose to determine the polynomial order by observing the regularity and the increase of the fitting cost. When using a fixed polynomial order under- or even overfitting could occur. Second, due to a fixed treshold on the fitting cost, arbitrary endpoints are detected for the segments, which are unsuitable as feature points. We propose to allow a variable segment thickness by detecting discontinuities and irregularities in the fitting cost. Our method is evaluated on the MPEG-7 core experiment CE-Shape-1 database part B [1]. In the experimental results, the edges are approximated closely by the polynomials of variable order. Furthermore, the polynomial segments have robust endpoints, which are suitable as feature points. When comparing adaptive constructive polynomial fitting (ACPF) to non-adaptive constructive polynomial fitting (NACPF), the average Hausdorff distance per segment decreases by 8.85% and the object recognition rate increases by 10.24%, while preserving simplicity and computational efficiency.

Image registration using uncertainty transformations

In this work we introduce a new technique for a frequently encountered problem in computer vision: image registration. The registration is computed by matching features, points and lines, in the reference image to their corresponding features in the test image among many candidate matches. Convex polygons are used to captivate the uncertainty of the transformation from the reference features to uncertainty regions in the test image in which candidate matches are to be found. We present a simple and robust method to check the consistency of the uncertainty transformation for all possible matches and construct a consistency graph. The distinction between the good matches and the rest can be computed from the information of the consistency graph. Once the good matches are determined, the registration transformation can be easily computed.