Irregular Pyramids are powerful hierarchical structures in pattern recognition and image processi... more Irregular Pyramids are powerful hierarchical structures in pattern recognition and image processing. They have high potential of parallel processing that makes them useful in processing of a huge amount of digital data generated every day. This paper presents a fast method for constructing an irregular pyramid over a binary image where the size of the images is more than 2000 in each of 2/3 dimensions. Selecting the contraction kernels (CKs) as the main task in constructing the pyramid is investigated. It is shown that the proposed fast labeled spanning tree (FLST) computes the equivalent contraction kernels (ECKs) in only two steps. To this purpose, first, edges of the corresponding neighborhood graph of the binary input image are classified. Second, by using a total order an efficient function is defined to select the CKs. By defining the redundant edges, further edge classification is performed to partition all the edges in each level of the pyramid. Finally, two important applications are presented : connected component labeling (CCL) and distance transform (DT) with lower parallel complexity 𝒪(𝑙𝑜 𝑔(𝛿)) where the 𝛿 is the diameter of the largest connected component in the image.
2021 5th International Conference on Pattern Recognition and Image Analysis (IPRIA), 2021
This paper presents a new logarithmic-time algorithm which simultaneously assigns labels to all c... more This paper presents a new logarithmic-time algorithm which simultaneously assigns labels to all connected components of a binary image in parallel. The irregular graph pyramid of an input binary image is constructed based on the optimized combinatorial structure. The novel small built pyramid has only three levels and is created at worst case with O(log(N 2 )) complexity for a N × N -sized (2D) binary image. To assign a label to each connected component, instead of the common linear-time raster scan techniques (with complexity O(N 2 )), only two important movements, namely bottom-up and top-down traversing, are needed. First, in the bottom-up traversing, the redundant connections are removed and the contraction kernels are contracted. This results in a simpler graph at top of the pyramid each of its vertices has a unique label identifying corresponding connected component. Such reduced graph preserves all connecting relations including inclusions. Second, in the top-down traversing, each unique label propagates down into each individual corresponding pixel at the base level. The complexity of the labeling propagation procedure in worst cases is O(log(image -size)). The GPU implementation of the algorithm has high performance and the bottleneck is the bandwidth of the memory or equivalently the number of available independent processing elements. Finally, the experimental results show the proposed algorithm outperforms the other state-of-the-art methods.
Tracking of articulated objects is a challenging task in Computer Vision. A highly target specifi... more Tracking of articulated objects is a challenging task in Computer Vision. A highly target specific model can improve the robustness of the tracking by eliminating or reducing the ambiguities in the association task. This paper presents a flexible framework, which allows to build target specific, part-based models for arbitrary articulated objects. The rigid parts are described by hierarchical spring systems in form of attributed graph pyramids and connected via articulation points, which transfer position information between the adjacent parts.
In this paper, we investigate the problem of analyzing the shape of obstacle-avoiding paths in a ... more In this paper, we investigate the problem of analyzing the shape of obstacle-avoiding paths in a space. Given a d-dimensional space with holes, representing obstacles, we ask if certain paths are equivalent, informally if one path can be continuously deformed into another, within this space. Algebraic topology is used to distinguish between topologically different paths. A compact yet complete signature of a path is constructed, based on cohomology theory. Possible applications include assisted living, residential, security and environmental monitoring. Numerical results will be presented in the final version of this paper.
Object tracking is the complex task of following given objects in a video stream. In this work we... more Object tracking is the complex task of following given objects in a video stream. In this work we present an algorithm that combines an optical flow based feature tracker with image color segmentation. The goal is to build a feature model and reconstruct feature points when they are lost due to occlusion or tracking errors. The feature points are tracked from frame to frame. Additionally, we segment each frame with the graph-based segmentation method. Optical flow and segmentation are then combined to track an object in a video scene. By using this strategy, occlusion and slight rotation or deformation can be handled. The tracker is evaluated on an artificial video sequence of moving balls and on real-world sequences of a moving person.
We present a new method to determine contraction kernels for the construction of graph pyramids. ... more We present a new method to determine contraction kernels for the construction of graph pyramids. The new method works with undirected graphs and yields a reduction factor of at least 2.0. This means that with our method the number of vertices in the subgraph induced by any set of contractible edges is reduced to half or less by a single parallel contraction. Our method yields better reduction factors than the stochastic decimation algorithm, in all tests. The lower bound of the reduction factor becomes crucial with large images.
The region's internal properties (color, texture, ...) help to identify them and their external r... more The region's internal properties (color, texture, ...) help to identify them and their external relations (adjacency, inclusion, ...) are used to build groups of regions having a particular consistent meaning in a more abstract context. Low-level cue image segmentation in a bottom-up way, cannot and should not produce a complete final "good" segmentation. We present a hierarchical partitioning of images using a pairwise similarity function on a graph-based representation of an image. The aim of this paper is to build a minimum weight spanning tree (MST ) of an image in order to find region borders quickly in a bottom-up 'stimulus-driven' way based on local differences in a specific feature.
Proceedings 15th International Conference on Pattern Recognition. ICPR-2000
In this paper a framework is presented that produces the mosaic corresponding to the background o... more In this paper a framework is presented that produces the mosaic corresponding to the background object of an image sequence. It is based on the dominant motion assumption, which states that the background has a parametric motion and occupates the main part of the images. The foreground objects are localised by their different motion. This localisation is computed together with the background motion in an iterative method. The regions corresponding to the background are then pasted onto the mosaic using classic methods adapted to object elimination or a new mosaicking method based on a striping that takes the foreground objects localisation into account.
Graph models offer high representational power and useful structural cues. Unfortunately, trackin... more Graph models offer high representational power and useful structural cues. Unfortunately, tracking objects by matching graphs over time is in general NP-hard. Simple appearance-based trackers are able to find temporal correspondences fast and efficient, but often fail to overcome challenging situations like occlusions, distractors and noise. This paper proposes an approach, where an attributed graph is used to represent the structure of the target object and multiple, simple trackers in combination with structural cues replace the costly graph matching. Thus, the strengths of both methodologies are combined to overcome their weaknesses. Experiments based on synthetic videos are used to evaluate two possible structural cues. Results show the superiority of the cue based on barycentric coordinates and the potential of the proposed tracking approach in challenging situations.
2006 Eighth International Symposium on Symbolic and Numeric Algorithms for Scientific Computing, 2006
Most of the existing work regarding topology preserving hierarchies is mainly preoccupied with 2D... more Most of the existing work regarding topology preserving hierarchies is mainly preoccupied with 2D domains. But recently attention has turned to 3D, and more generally, nD representations. Even more than in 2D, the necessity for reducing these representations exists and motivates the research in hierarchical structures i.e. pyramids. Using representations that support any dimension, like e.g. the combinatorial map, n dimensional irregular pyramids can be built, thus obtaining reduced representations of the original data, while preserving the topology. This paper presents 3D combinatorial maps and the primitive operations needed to simplify such representations. Minimal configurations of the three primitive topological configurations, simplex, hole, and tunnel, and two possible configurations for two tori are presented. Experimental results and possible applications show the potential of the approach.
We continue previous work about the combination of top-down and bottom-up adaptive segmentation t... more We continue previous work about the combination of top-down and bottom-up adaptive segmentation techniques, Voronoi diagrams and irregular pyramids. We extend our considerations to the dual irregular pyramid to overcome the problem of increasing degree inherent to the "classical" irregular pyramid. Experimental results are presented, the analysis of which reveals inconsistencies in the theory of dual irregular pyramids. The conclusion of the report outlines two strategies for research in view of a solution.
We present a hierarchical partitioning of images using a pairwise similarity function on a graph-... more We present a hierarchical partitioning of images using a pairwise similarity function on a graph-based representation of an image. This function measures the dierence along the
Dual graph contraction reduces the number of vertices and of edges of a pair of dual image graphs... more Dual graph contraction reduces the number of vertices and of edges of a pair of dual image graphs while, at the same time, the topological relations among the 'surviving' components are preserved. Repeated application produces a stack of successively smaller graphs: a pair of dual irregular pyramids. The process is controlled by selected decimation parameters which consist of a subset of surviving vertices and associated contraction kernels. Equivalent contraction kernels (ECKs) combine two or more contraction kernels into one single contraction kernel which generates the same result in one single dual contraction. Decimation parameters of any individual pyramid level can be reconstructed from the ECK of the pyramid's apex if both vertices and edges of this ECK receive labels indicating their annihilation level in the pyramid. This is a labeled spanning tree (LST) of the base graph which allows e cient design and control of di erent types of dual irregular pyramids. Since the LST determines the pyramid, primitive modi cations of the LST transform also pyramids into other pyramids on the same base graph. They open a large variety of possibilities to explore the domain of 'all' pyramids.
In this paper we focus on the problem of improving the performance of object tracking in motion s... more In this paper we focus on the problem of improving the performance of object tracking in motion sequences by exploiting the spatial and temporal structure of the scene. First we show typical examples where tracking methods not using structural information tend to fail. ...
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Papers by W. Kropatsch