Multi-channel Chan-Vese model for unsupervised segmentation of nuclei from breast histopathological images

Cartoon-texture evolution for two-region image segmentation

“…In order to make a fair comparison, all the algorithms presented in the next section use the stopping criterion (22), where we set maxit = 50 and tol = 10 −6 (tol = 10 −8 for the noisy images). The parameter λ in (1) and in (9), has a scaling role and was set according to the level of required details in the segmentation. In particular, in each test for CEN model we used the value proposed by the authors in the available code, which we indicate as λ CEN , based on this empirical rule: λ CEN = 10 a with a ∈ {−1, 0, 1} from larger to smaller regularization/smoothing.…”

“…Variational models, based on optimizing energy functionals, have been widely investigated, proving to be very effective on different images; curve evolution [5], anisotropic diffusion [6] and the Mumford-Shah model [7] are good representatives of these methods. Other recent approaches to image segmentation include learningbased methods, which often exploit deep-learning techniques [8][9][10]. However, in this case, a large amount of data must be available to train learning networks, thus making those approaches impractical in some applications.…”

“…These models are currently used in medical and astronomical application fields and have lately been associated with machine learning frameworks (see, e.g. [9,[18][19][20][21][22]). The Chan-Vese model is a special case of the most popular Mumford-Shah one [7] restricted to piecewise constant functions.…”

Cartoon-texture evolution for two-region image segmentation

“…Variational models, based on optimizing energy functionals, have been widely investigated, proving to be very effective on different images; curve evolution [4], anisotropic diffusion [5] and the Mumford-Shah model [6] are good representatives of these methods. Other recent approaches to image segmentation include learning-based methods, which often exploit deep-learning techniques [7][8][9], watershed [10], random walk methods [11], graph cuts [12,13], epidemiological models on images [14]. However, in this case, a large amount of data must be available to train learning networks, thus making those approaches impractical in some applications.…”

“…These models are currently used in medical and astronomical application fields and have lately been associated with machine learning frameworks (see, e.g. [8,[22][23][24][25][26]). The Chan-Vese model is a special case of the most popular Mumford-Shah one [6] restricted to piecewise constant functions.…”