Level set evolution without re-initialization: a new variational formulation

By Chunming Li, Changfeng Gui, Martin D. Fox. Computer Vision and Pattern Recognition, 2005

2,188 citations recorded by the source corpus.

In this paper, we present a new variational formulation for geometric active contours that forces the level set function to be close to a signed distance function, and therefore completely eliminates the need of the costly re-initialization procedure. Our variational formulation consists of an internal energy term that penalizes the deviation of the level set function from a signed distance function, and an external energy term that drives the motion of the zero level set toward the desired image features, such as object boundaries. The resulting evolution of the level set function is the gradient flow that minimizes the overall energy functional. The proposed variational level set formulation has three main advantages over the traditional level set formulations. First, a significantly larger time step can be used for numerically solving the evolution partial differential equation, and therefore speeds up the curve evolution. Second, the level set function can be initialized with general functions that are more efficient to construct and easier to use in practice than the widely used signed distance function. Third, the level set evolution in our formulation can be easily implemented by simple finite difference scheme and is computationally more efficient. The proposed algorithm has been applied to both simulated and real images with promising results.

Subfields: Biophysics, Computer Vision and Pattern Recognition

View Paper: https://www.semanticscholar.org/paper/d243b5eb81a8501cc0477c47a4ce7d4feb524aee

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Biophysics

In Computer Vision and Pattern Recognition

Citations in the corpus

TouchCut: Fast image and video segmentation using single-touch interaction (2014, methodology): “For our proposed formulation, as re-initialization is not needed due to the incorporation of distance regularization term Ed [42], the narrow band implementation is simple and straightforward.”
Distance Regularized Level Set Evolution and Its Application to Image Segmentation (2010, methodology): “The level set evolution without reinitialization in our preliminary work [27] is a special case of the DRLSE in (13).”
Minimization of Region-Scalable Fitting Energy for Image Segmentation (2008, background): “Existing active contour models can be categorized into two major classes: edge-based models [3], [10]–[12], [18], [19], [28], [30], and region-based models [4], [23], [25]–[27], [29].”
Active contours driven by local image fitting energy (2010, methodology): “[9] proposed a variational formulation penalizing the deviation of the level set function from an SDF, which is useful in the application of variational level set methods but cannot be applied to the pure partial differential equation (PDE) driven level set methods.”
Implicit Active Contours Driven by Local Binary Fitting Energy (2007, methodology): “In order to ensure stable evolution of the level set function φ, we add the distance regularizing term in Li et al’s variational level set formulation [9] to penalize the deviation of the level set function φ from a signed distance function.”
Semi-supervised Medical Image Segmentation through Dual-task Consistency (2020, background): “In existing works, pixel-wise classiﬁcation for segmentation has been widely studied while level-set function (Li et al. 2005) is a traditional task that captures geometric active contours and distance information, which rejuvenates recently when combining with CNN (Wang et al. 2020).”
Active contours with selective local or global segmentation: A new formulation and level set method (2010, background): “According to the nature of constraints, the existing ACMs can be categorized into two types: edge-based models [1,3,4,6,10,12,18,20] and region-based models [5,7,8,11,14–17].”
Wound intensity correction and segmentation with convolutional neural networks (2017, background): “Li et al. [15] proposed the local binary ﬁtting (LBF) model by embedding local information in a level set model (LSM).”
Plant phenotyping with low cost digital cameras and image analytics (2009, methodology): “For the new night picture, the segmentation mask of the latest daytime image is used to initialize a level set segmentation algorithm (Li et al. 2005).”
Active contours driven by local Gaussian distribution fitting energy (2009, background): “The level set function f can be simply initialized as a binary step function as in [7], which takes a negative constant value c0 inside the region R0 and a positive constant value c0 outside it.”
Integrating spatial fuzzy clustering with level set methods for automated medical image segmentation (2011, methodology): “It adopted the fast level set algorithm as in references [23,24] for the curve optimization, where the initialization was by manual demarcation, intensity thresholding and spatial fuzzy clustering.”
Automated gland and nuclei segmentation for grading of prostate and breast cancer histopathology (2008, methodology): “The evolution of φ is then described by a level-set formulation adopted from [8]:”
DeepCrack: Learning Hierarchical Convolutional Features for Crack Detection (2019, background): “While for contour detection, the ratio contour [25], level set [26], [27] and untangling cycles [28] are part of the representatives, which model the line clutters with graph, and minimize the energy function to infer out the contour.”
Deep Level Sets for Salient Object Detection (2017, methodology): “Traditionally, in level set methods for image segmentation [8, 28], an initial level sets φ0 and an image are given as input.”