Article

Random walks for image segmentation. TPAMI, 28, 1768-1783

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Abstract

A novel method is proposed for performing multilabel, interactive image segmentation. Given a small number of pixels with user-defined (or predefined) labels, one can analytically and quickly determine the probability that a random walker starting at each unlabeled pixel will first reach one of the prelabeled pixels. By assigning each pixel to the label for which the greatest probability is calculated, a high-quality image segmentation may be obtained. Theoretical properties of this algorithm are developed along with the corresponding connections to discrete potential theory and electrical circuits. This algorithm is formulated in discrete space (i.e., on a graph) using combinatorial analogues of standard operators and principles from continuous potential theory, allowing it to be applied in arbitrary dimension on arbitrary graphs.

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... For instance, Lin et al. [6] proposed a GrabCut [7]-based method called ScribbleSup to enlarge annotations from scribbles to unlabelled pixels. Vernaza et al. [8] integrated Random Walker [9] with edge detection and estimated the uncertainty when propagating labelled pixels to unknown regions. Tang et al. [10] integrated the Conditional Random Fields (CRF) [11]-based refining into the model training with a KernelCut [12]-based regularization loss. ...
... With the growth of advanced neural networks, the exploration of graphical-based preprocessing methods in conjunction with neural networks and their application to medical image segmentation tasks were emerging. Can et al. [13] explored scribble-supervised prostate MRI segmentation, consisting of Random Walker [9] as a pre-processing step for generating seed area via region growing, and dense CRF [14] as a post-processing step for joint recurrent neural network training. They achieved 0.772 Dice on prostate segmentation. ...
... Several state-of-the-art scribble-supervised segmentation methods were implemented in this study, including ScribbleSup [6], RandomWalks [9], USTM-Net [30], Sribble2Label [28], Gated CRF [43], MumfordLoss [44], EntropyMini [45], Regularized Loss [10], WSL4MIS [4], CycleMix [20], Puzzle Mix [24], ShapePU [33], CVIR [46], nnPU [47] and ZScribbleSeg [48]. Tables 2 and 3 reported the results on the ACDC dataset and MSCMR dataset, respectively. ...
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The transition in medical image segmentation from fine-grained to coarse-grained annotation methods, notably scribble annotation, offers a practical and efficient preparation for deep learning applications. However, these methods often compromise segmentation precision and result in irregular contours. This study targets the enhancement of scribble-supervised segmentation to match the accuracy of fine-grained annotation. Capitalizing on the consistency of target shapes across unpaired datasets, this study introduces a shape-aware scribble-supervised learning framework (MaskMixAdv) addressing two critical tasks: (1) Pseudo label generation, where a mixup-based masking strategy enables image-level and feature-level data augmentation to enrich coarse-grained scribbles annotations. A dual-branch siamese network is proposed to generate fine-grained pseudo labels. (2) Pseudo label optimization, where a CNN-based discriminator is proposed to refine pseudo label contours by distinguishing them from external unpaired masks during model fine-tuning. MaskMixAdv works under constrained annotation conditions as a label-efficient learning approach for medical image segmentation. A case study on public cardiac MRI datasets demonstrated that the proposed MaskMixAdv outperformed the state-of-the-art methods and narrowed the performance gap between scribble-supervised and mask-supervised segmentation. This innovation cuts annotation time by at least 95%, with only a minor impact on Dice performance, specifically a 2.6% reduction. The experimental outcomes indicate that employing efficient and cost-effective scribble annotation can achieve high segmentation accuracy, significantly reducing the typical requirement for fine-grained annotations.
... Image segmentation has promising applications in various domains, such as medical diagnostics [1], autonomous driving [2], and security surveillance [3]. Traditional image segmentation methods [4][5][6][7] typically rely on handcrafted features and complex post-processing techniques. These methods struggle to manage complex scenes and diverse objects. ...
... Boykov et al. [4] introduce the graph cut method, which connects all pixel nodes and assigns energy or weights to these connections. Grady et al. [5] proposed the random walks algorithm in 2006, modeling the image as an undirected graph and solving the Dirichlet problem to achieve segmentation. Bai et al. [6] developed geodesic matting in 2009, which uses a graph-based approach to estimate the kernel density of unknown pixels from labeled points. ...
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... [3,17,18] The random walk algorithm has been applied to various fields, including image segmentation. [19] One advantage of random walk algorithm lies in that it can maintain correlation of partition results over time, because the result will strongly depend on the initial location of random walkers. When the locations of random walkers are properly chosen, the shape of congested partitions will be similar and correlated. ...
... The task can be modeled as a discrete Dirichlet problem. [19] The preliminary partitioning can be described as follows. First mark the random walkers X M , then compute the probability that all the unmarked points X U in the undirected graph first randomly wander to a differently marked point, and then take the label s as corresponding to the largest probability of the classification to which the point belongs. ...
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The successful application of perimeter control of urban traffic system strongly depends on the macroscopic fundamental diagram of the targeted region. Despite intensive studies on the partitioning of urban road networks, the dynamic partitioning of urban regions reflecting the propagation of congestion remains an open question. This paper proposes to partition the network into homogeneous sub-regions based on random walk algorithm. Starting from selected random walkers, the road network is partitioned from the early morning when congestion emerges. A modified Akaike information criterion is defined to find the optimal number of partitions. Region boundary adjustment algorithms are adopted to optimize the partitioning results to further ensure the correlation of partitions. The traffic data of Melbourne city are used to verify the effectiveness of the proposed partitioning method.
... In contrast, interactive segmentation methods [7], which leverage users' expertise and experience to obtain more accurate segmentation results, are more practical in clinical applications. Interactive segmentation allows additional user prompts (such as bounding boxes [8][9][10], scribbles [11][12][13], and clicks [14][15][16][17]) to effectively segment target objects in images. Among these, click-based methods are the most widely used due to their simplicity and well-established training and evaluation protocols. ...
... Interactive segmentation (IS) is a highly active research area focusing on the dynamic interaction between humans and machines. Traditional interactive segmentation methods [10,12,32,33] employ graphs defined on image pixels to address segmentation challenges. However, these approaches rely solely on low-level features, rendering them inadequate for handling complex environments. ...
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Interactive segmentation methods utilize user-provided positive and negative clicks to guide the model in accurately segmenting target objects. Compared to fully automatic medical image segmentation, these methods can achieve higher segmentation accuracy with limited image data, demonstrating significant potential in clinical applications. Typically, for each new click provided by the user, conventional interactive segmentation methods reprocess the entire network by re-inputting the click into the segmentation model, which greatly increases the user’s interaction burden and deviates from the intended goal of interactive segmentation tasks. To address this issue, we propose an efficient segmentation network, ESM-Net, for interactive medical image segmentation. It obtains high-quality segmentation masks based on the user’s initial clicks, reducing the complexity of subsequent refinement steps. Recent studies have demonstrated the strong performance of the Mamba model in various vision tasks; however, its application in interactive segmentation remains unexplored. In our study, we incorporate the Mamba module into our framework for the first time and enhance its spatial representation capabilities by developing a Spatial Augmented Convolution (SAC) module. These components are combined as the fundamental building blocks of our network. Furthermore, we designed a novel and efficient segmentation head to fuse multi-scale features extracted from the encoder, optimizing the generation of the predicted segmentation masks. Through comprehensive experiments, our method achieved state-of-the-art performance on three medical image datasets. Specifically, we achieved 1.43 NoC@90 on the Kvasir-SEG dataset, 1.57 NoC@90 on the CVC-ClinicDB polyp segmentation dataset, and 1.03 NoC@90 on the ADAM retinal disk segmentation dataset. The assessments on these three medical image datasets highlight the effectiveness of our approach in interactive medical image segmentation.
... Semiautomatic segmentation relies on the prior to initialize the segmentation and implements algorithm to execute the segmentation (Hong-Seng, Sayuti, and Karim 2017). Famous semiautomatic segmentation algorithms include Graph Cuts (Boykov and Funka-Lea 2006), Random Walks (Grady 2006), and Watershed (Bertrand 2005). Generic automatic segmentation employs atlas or feature extractor and classifier to extract target organ. ...
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Medical image segmentation is prerequisite in computer‐aided diagnosis. As the field experiences tremendous paradigm changes since the introduction of foundation models, technicality of deep medical segmentation model is no longer a privilege limited to computer science researchers. A comprehensive educational resource suitable for researchers of broad, different backgrounds such as biomedical and medicine, is needed. This review strategically covers the evolving trends that happens to different fundamental components of medical image segmentation such as the emerging of multimodal medical image datasets, updates on deep learning libraries, classical‐to‐contemporary development in deep segmentation models and latest challenges with focus on enhancing the interpretability and generalizability of model. Last, the conclusion section highlights on future trends in deep medical segmentation that worth further attention and investigations.
... In this study, genetic algorithm [71], particle swarm optimization [72], gray wolf optimizer [73], cuckoo search algorithm [74], metaheuristic algorithms, and graph cut [75] were used to perform the segmentation task. In addition, the random walker [76] algorithm is included. Common problems in segmentation applications include lowcontrast images, image quality, heterogeneity of brain tissue, and ambiguity of tumors/lesions. ...
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... A machine learning segmentation method (IPSDK Explorer https://www.reactivip.com/) was used to segment the μCT images. This kind of pixel-based segmentation uses different feature maps (volumes) and a random walker in combination with a set of hand-labeled phase identifications (Grady, 2006). The algorithm segments the image based on the CT number and textural features, as shown in Figure 5, by the overlapping histograms showing voxel values and assigned phases for each sample, along with 2D slices of segmented samples. ...
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... Segmentation refers to the general methods that involve dividing an analyzing an image and pulling out pertinent data about certain parts of the picture, like lines, areas and items, as well as how they are connected, see (Felzenszwal-Huttenlochter, 2004, Ford-Fulkerson, 1962, Grady, 2006, Khalifa-Badr 2023. It is essentially a procedure for information. ...
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... Recently, models like detection transformer (DETR) [26] have shown significant progress in 2D segmentation [21,25,[27][28][29][30][31][32][33], leveraging the Transformer architecture [34] for enhanced performance. In the realm of interactive segmentation [35][36][37][38][39][40], where user input guides the segmentation process, a variety of innovations have emerged. A notable example is the Segment Anything Model (SAM) [37], which has a prompt-based approach. ...
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... Patches [19] divides the image into grids where each cell is the same size. Quickshift [27] connects similar neighboring pixels into a common superpixel. Watershed [46] simulates flooding on a topographic surface. ...
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