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The critical task of recognizing human–object interactions (HOI) finds its application in the domains of surveillance, security, healthcare, assisted living, rehabilitation, sports, and online learning. This has led to the development of various HOI recognition systems in the recent past. Thus, the purpose of this study is to develop a novel graph-based solution for this purpose. In particular, the proposed system takes sequential data as input and recognizes the HOI interaction being performed in it. That is, first of all, the system pre-processes the input data by adjusting the contrast and smoothing the incoming image frames. Then, it locates the human and object through image segmentation. Based on this, 12 key body parts are identified from the extracted human silhouette through a graph-based image skeletonization technique called image foresting transform (IFT). Then, three types of features are extracted: full-body feature, point-based features, and scene features. The next step involves optimizing the different features using isometric mapping (ISOMAP). Lastly, the optimized feature vector is fed to a graph convolution network (GCN) which performs the HOI classification. The performance of the proposed system was validated using three benchmark datasets, namely, Olympic Sports, MSR Daily Activity 3D, and D3D-HOI. The results showed that this model outperforms the existing state-of-the-art models by achieving a mean accuracy of 94.1% with the Olympic Sports, 93.2% with the MSR Daily Activity 3D, and 89.6% with the D3D-HOI datasets.

Dijkstra’s algorithm (DA) is one of the most useful and efficient graph-search algorithms, which can be modified to solve many different problems. It is usually presented as a tool for finding a mapping which, for every vertex v , returns a shortest-length path to v from a fixed single source vertex. However, it is well known that DA returns also a correct optimal mapping when multiple sources are considered and for path-value functions more general than the standard path-length. The use of DA in such general setting can reduce many image processing operations to the computation of an optimum-path forest with path-cost function defined in terms of local image attributes. In this paper, we describe the general properties of a path-value function defined on an arbitrary finite graph which, provably, ensure that Dijkstra’s algorithm indeed returns an optimal mapping. We also provide the examples showing that the properties presented in a 2004 TPAMI paper on the image foresting transform, which were supposed to imply proper behavior of DA, are actually insufficient. Finally, we describe the properties of the path-value function of a graph that are provably necessary for the algorithm to return an optimal mapping.

The distance transform is a crucial technique in binary image processing, assigning the distance to the nearest contour to each foreground pixel. In this extended version of our previous work, we enhance our method for computing the maximum distance transform (DT) value, now utilizing the optimized differential image foresting transform (DIFT) and improved contour extraction processes. These advancements enable more efficient computation of the maximum DT value across all connected components of a grayscale image, significantly reducing computational time by intelligently reusing DIFT trees rooted at contour points (DIFT seeds). Our optimized algorithm now achieves processing speeds that are twice as fast as our previous differential method. The proposed attribute, maximum distance, which measures the thickness of objects within the image, has proven pivotal in different image processing approaches. We showcase this through detailed illustrations of attribute opening, extinction value filters, watershed, and ultimate attribute openings.

Image foresting transform (IFT) is a graph-based framework to develop image operators based on optimum connectivity between a root set and the remaining nodes, according to a given path-cost function. Oriented image foresting transform (OIFT) was proposed as an extension of some seeded IFT-based segmentation methods to directed graphs, enabling them to support the processing of global object properties, such as connectedness, shape constraints, boundary polarity, and hierarchical constraints, allowing their customization to a given target object. OIFT lies in the intersection of generalized graph cut and general fuzzy connectedness frameworks, inheriting their properties. Its returned segmentation is optimal, with respect to an appropriate graph cut measure, among all segmentations satisfying the given constraints. In this work, we propose differential oriented image foresting transform, which allows multiple OIFT executions for different root sets, making the processing time proportional to the number of modified nodes. Experimental results show considerable efficiency gains over the sequential flow of OIFTs in image segmentation, while maintaining a good treatment of tie zones. We also demonstrate that the differential flow makes it feasible to incorporate the prior knowledge about the maximum allowable size for the segmented object, thus avoiding false positive errors in the segmentation of multi-dimensional images. We also propose an algorithm to efficiently create a hierarchy map that encodes area-constrained OIFT results for all possible thresholds, facilitating the quick selection of the object of interest.

The goal of this work is to describe an efficient algorithm for finding a binary segmentation of an image such that the indicated object satisfies a novel high-level prior, called local band, LB, constraint; the returned segmentation is optimal, with respect to an appropriate graph-cut measure, among all segmentations satisfying the given LB constraint. The new algorithm has two stages: expanding the number of edges of a standard edge-weighted graph of an image; applying to this new weighted graph an algorithm known as an oriented image foresting transform, OIFT. In our theoretical investigation, we prove that OIFT algorithm belongs to a class of general fuzzy connectedness algorithms and so has several good theoretical properties, like robustness for seed placement. The extension of the graph constructed in the first stage ensures, as we prove, that the resulted object indeed satisfies the given LB constraint. We also notice that this graph construction is flexible enough to allow combining it with other high-level constraints. Finally, we experimentally demonstrate that the LB constraint gives competitive results as compared to geodesic star convexity, boundary band, and hedgehog shape prior, all implemented within OIFT framework and applied to various scenarios involving natural and medical images.

Image segmentation can be elegantly solved by optimum-path forest and minimum cut in graph. Given that both approaches exploit similar image graphs, some comparative analysis is expected between them. We clarify their differences and provide their comparative analysis from the theoretical point of view, for the case of binary segmentation (object/background) in which hard constraints (seeds) are provided interactively. Particularly, we formally prove that some optimum-path forest methods from two distinct region-based segmentation paradigms, with internal and external seeds and with only internal seeds, indeed minimize some graph-cut measures. This leads to a proof of the necessary conditions under which the optimum-path forest algorithm and the min-cut/max-flow algorithm produce exactly the same segmentation result, allowing a comparative analysis between them.

Anatomical structures and tissues are often hard to be segmented in medical images due to their poorly defined boundaries, i.e., low contrast in relation to other nearby false boundaries. The specification of the boundary polarity can help alleviate a part of this problem. In this work, we discuss how to incorporate this property in the relative fuzzy connectedness (RFC) framework. We include a theoretical proof of the optimality of the new algorithm, named oriented relative fuzzy connectedness (ORFC), in terms of an oriented energy function subject to the seed constraints, and show its usage to devise powerful hybrid image segmentation methods. The methods are evaluated using medical images of MRI and CT of the human brain and thoracic studies.

The Image Foresting Transform (IFT) is a tool for the design of image processing operators based on connectivity, which reduces image processing problems into an optimum-path forest problem in a graph derived from the image. A new image operator is presented, which solves segmentation by pruning trees of the forest. An IFT is applied to create an optimum-path forest whose roots are seed pixels, selected inside a desired object. In this forest, object and background are connected by optimum paths (leaking paths), which cross the object’s boundary through its “most weakly connected” parts (leaking pixels). These leaking pixels are automatically identified and their subtrees are eliminated, such that the remaining forest defines the object. Tree pruning runs in linear time, is extensible to multidimensional images, is free of ad hoc parameters, and requires only internal seeds, with little interference from the heterogeneity of the background. These aspects favor solutions for automatic segmentation. We present a formal definition of the obtained objects, algorithms, sufficient conditions for tree pruning, and two applications involving automatic segmentation: 3D MR-image segmentation of the human brain and image segmentation of license plates. Given that its most competitive approach is the watershed transform by markers, we also include a comparative analysis between them.

This work reviews the watershed in the graph framework of a shortest-path forest problem using a lexicographic path cost formulation. This formulation reflects the behavior of the ordered queue-based watershed algorithm. This algorithm is compared with our proposed shortest-path forest (IFT-Image Foresting Transform), concluding that the watershed is a special case of that. Recently many different watershed approaches are being used. We point out that in some cases the watershed algorithm does not keep the optimality of the shortest-path forest solution unless the IFT algorithm is used. The main difference between the algorithms is related to permanently labeling a pixel when inserting or removing it from the queue. The watershed based on the pixel dissimilarity using IFT can segment one-pixel width regions while keeping the optimality of the shortest-path forest solution.