Image segmentation via functionals based on boundary functions

Breast ultrasound (BUS) imaging is commonly used in the early detection of breast cancer as a portable, valuable, and widely available diagnosis tool. Automated BUS image classification and segmentation can assist radiologists in making accurate and fast decisions. Recent studies illustrate that tumor, peritumoral, and background regions of BUS images provide valuable information for BUS image segmentation or classification. However, few studies have investigated the influence of these three regions on multi-task learning. In this study, we propose an RMTL-Net to simultaneously segment tumor regions and classify tumors in BUS images into benign or malignant categories. To improve both segmentation and classification performance, we design a regional attention (RA) module that employs the predicted probability maps to automatically guide the classifier to learn important category-sensitive information in the tumor, peritumoral, and background regions and seamlessly fuse them to obtain a better feature representation. We conduct detailed ablation experiments of the proposed RA module and comparative experiments with four recent state-of-the-art peer multi-task learning methods, three single-task segmentation methods, and four single-task classification methods on two public BUS datasets. Experimental results show that the proposed RMTL-Net achieves the best overall segmentation and classification accuracy in terms of five segmentation metrics and six classification metrics.

Abstract—This research presents an integrated framework for satellite image retrieval, segmentation, and visualization, utilizing Python-based algorithms and geospatial data processing methods. It incorporates Google Maps-based image acquisition, a Tkinter-powered interactive GUI, and the U-Net segmentation model to efficiently process satellite imagery. Satellite image segmentation, powered by U-Net, plays a vital role in geospatial analysis, enabling automated classification and extraction of key features from high-resolution imagery. The framework facilitates seamless high-resolution map generation, segmentation, and an- alytical visualization through interactive tools like bar graphs and pie charts. By leveraging U-Net’s robust architecture, this implementation enhances segmentation accuracy and supports applications in urban planning, environmental monitoring, and disaster management. Through the automation of retrieval, processing, and visualization of satellite imagery, this research advances geospatial intelligence and provides a scalable solution for efficient image segmentation workflows. Keywords—Satellite Image Segmentation, Land Cover Classi- fication, Remote Sensing, Image Processing, Semantic Segmen- tation, Deep Learning Models, Convolutional Neural Networks (CNNs), U-Net Architecture, Geospatial Analysis, Land Use Analysis

In this paper, we use a variational Bayesian framework for color image segmentation. Each image is represented in the Luv color coordinate system before being segmented by the variational algorithm. The model chosen to describe the color images is a Gaussian mixture model. The parameter estimation uses variational learning by taking into account the uncertainty in parameter estimation. In the variational Bayesian approach, we integrate over distributions of parameters. We propose a maximum log-likelihood initialization approach for the variational expectation-maximization (VEM) algorithm and we apply it to color image segmentation. The segmentation task in our approach consists of the estimation of the distribution hyperparameters.

LSRML: A latent space regularization based meta-learning framework for MR image segmentation

Automatic segmentation of Magnetic Resonance Images (MRI) for tissue classification becomes more challenging when the image is corrupted with noise and intensity non-uniformity (INU). Several fuzzy clustering based statistical retrospective methods exist for simultaneous correction and segmentation of images but most of them fail to be robust in presence of noise, outliers and INU artifacts. In this paper, a hybridization of rough c-means and spatial fuzzy c-means clustering is presented whose objective function has been modified to accommodate INU field as well. While the membership function of fuzzy sets enables efficient handling of overlapping partitions, the concept of lower and upper approximations of rough sets deals with uncertainty, vagueness, and incompleteness in class definition. The experiments conducted on brain MR images show promising results in terms of segmentation accuracy and class separability. The usefulness of proposed algorithm is also investigated on high field MR images. The proposed algorithm Rough-Theoretic Bias-Corrected Fuzzy C-Means Algorithm (R-BCFCM) has significant performance improvement over other similar methods from rough-fuzzy family and can be employed for MRI corrupted with high intensity non-uniformity and noise.

We propose error backpropagation using the absolute error function as an objective function. The error backpropagation is the most popular learning algorithm for multi-layered neural networks. In the error backpropagation, the square error function is usually used as the objective function. But a square function has a drawback in which it is enormously large if the data set includes a few anomalous data, which may be observational errors. On the other hand, the absolute error function is less affected by such data. But since the absolute error function is not differentiable, the standard backpropagation's way cannot be applied directly by using an absolute error function as an objective function. Therefore, we first introduce differentiable approximate functions for the absolute value function. The purpose of introducing an approximate function is to construct a differentiable error function which is close to the absolute error function. Then we propose an error backpropagation algorithm minimizing a differentiable approximate error function. Some computational experiments indicate that the proposed method is practically efficient. In particular, it is observed that the method is more robust and learns faster than the backpropagation with the square error function when teacher signals include some incorrect data.

This paper proposes a novel framework for image segmentation through a unified model-based and pixel-driven integrated graphical model. Prior knowledge is expressed through the deformation of a discrete model that consists of decomposing the shape of interest into a set of higher order cliques (triplets). Such decomposition allows the introduction of region-driven image statistics as well as pose-invariant (i.e. translation, rotation and scale) constraints whose accumulation introduces global deformation constraints on the model. Regional triangles are associated with pixels labeling which aims to create consistency between the model and the image space. The proposed formulation is pose-invariant, can integrate regional statistics in a natural and efficient manner while being able to produce solutions unobserved during training. The challenging problem of tagged cardiac MR image segmentation is used to demonstrate the performance potentials of the method.

In this paper, we review some mathematical models in medical image processing. Due to the superiority in modeling and computation, variational methods have been proven to be powerful techniques, which have been extremely popular and dramatically improved in the past two decades. On one hand, many models have been proposed for nearly all kinds of applications. On the other hand, a lot of models can be globally optimized and also many computation tools have been introduced. Under the variational framework, we focus on two basic problems in medical imaging: image restoration and segmentation, which are core components for kinds of specific tasks. For image restoration, we discuss some models on both additive and multiplicative noises. For image segmentation, we review some models on both whole image segmentation and specific target delineation, with the later being a key step in computer aided surgery. Additionally, we present some models on liver delineation and give their applications to living donor liver transplantation.

The purpose of this study was to evaluate a semi-supervised Mean Teacher (MT) framework for semantic segmentation of cataract surgical images, addressing the challenge of limited labeled data in real-world clinical applications. We adapted the MT framework for four-class segmentation of the iris, pupil, intraocular lens, and surgical instruments using a small labeled set and 40,000 unlabeled Cataract-1K frames. Performance was assessed using Dice Similarity Coefficient (DSC) and the 95th percentile Hausdorff Distance (HD95). MT was compared with a fully supervised UNet under varying labeled and unlabeled conditions, and additional baselines provided broader context. Ablation studies evaluated noise types and key hyperparameters, including consistency weight (λ) and exponential moving average (EMA) decay (α). Internal validation used Cataract-1K, and external testing was done on CaDIS and CatInstSeg. Our MT model consistently outperformed the supervised UNet baseline. With 100 labeled images and 40,000 unlabeled frames, MT achieved a DSC of 0.76 ± 0.12 compared to UNet with 0.59 ± 0.17 (t = 21.23, P < 0.05). On CaDIS and CatInstSeg, MT reached DSCs of 0.69 ± 0.17 and 0.71 ± 0.20, outperforming UNet at 0.62 ± 0.08 and 0.64 ± 0.23. Optimal performance was observed with λ = 0.1, α = 0.995, and Gaussian noise σ = 15. The MT framework provides an effective semi-supervised solution for surgical image segmentation with limited annotations. Full source code and utility scripts will be released upon acceptance at: https://github.com/mahtabfaraji1/Semi-supervised-segmentation-of-cataract-surgical-images. Accurate segmentation of ocular anatomy and instruments supports surgical guidance, intraoperative decision making, and training tools in data-limited clinical environments.

Neighbouring-slice Guided Multi-View Framework for brain image segmentation

Multilevel thresholding for image segmentation is a crucial process in several applications such as feature extraction and pattern recognition. The meticulous search for the best values for the optimization of fitness function using classical operations needs profuse computational time, which also results in inaccuracy and instability. In this paper, a new beta differential evolution (BDE)-based fast color image multilevel thresholding scheme using two objective functions has been presented. The optimal threshold values are determined by maximizing Kapur’s and Tsallis entropy (entropy criterion) thresholding functions coupled with BDE algorithm. The efficiency of the proposed method is examined over existing multilevel thresholding methods such as artificial bee colony, particle swarm optimization, wind-driven optimization and differential evolution. These approaches are aimed to determine optimum threshold values at different levels of thresholding for color image segmentation. The proficiency of the presented methodology is demonstrated visually and computationally on five real-life true color images as well as four satellite images. Experimental outcomes are exhibited in terms of the optimal threshold value, best objective function and computational cost (in seconds) for each method at different thresholding levels. Afterward, the proposed scheme is examined intensively regarding the superiority of quality. The experimentally evaluated results show that the proposed BDE-based approach for multilevel color image segmentation can accurately and efficiently examine for multiple thresholds, which are near to optimal ones searched using an exhaustive search process.

This paper presents an extended variant of the distance-weighted exponential natural evolution strategy (DXNES) that works well in uncertain environments. Since we often face objective functions with uncertain parameters in real-world problems, function optimization in uncertain environments is an important problem. The covariance matrix adaptation evolution strategy (CMA-ES) and DX-NES have been proposed as promising methods for function optimization in deterministic environments. The performance of these methods, however, deteriorates in uncertain environments. The uncertain handling CMA-ES (TIH-CMA-ES) has been proposed as an extended variant of CMA-ES for uncertain environments and has shown relatively good performance on problems with uncertain parameters. In this paper, we propose an extended variant of DX-NES named DX-NES for uncertain environments (DX-NES-TIE). DX-NES-TIE approximates the objective function by a quadratic function. DXNES-TIE uses approximation function values for updating the mutation distribution if the noise is strong; otherwise it uses observed objective function values. The strength of the noise is quantified by using the approximation function and the evolution path. Through numerical experiments on 20-dimensional uncertain benchmark problems, we demonstrate that DX-NES-TIE can find ten to 2,000 times as accurate solutions as TIH-CMA-ES can. We also apply DX-NES-TIE to 80-dimensional problems and confirm that DX-NES-TIE is scalable with respect to problem dimensionality.

In the current vast image segmentation literature, there is a serious lack of methods that would allow theoretical comparison of the algorithms introduced by using different mathematical methodologies. The main goal of this article is to introduce a general theoretical framework for image segmentation that would allow such comparison. The framework is based on the formal definitions designed to answer the following fundamental questions: What is the relation between an idealized image and its digital representation? What properties a segmentation algorithm must satisfy to be acknowledged as acceptable? What does it mean that a digital image segmentation algorithm truly approximates an idealized segmentation model? We use the formulated framework to analyze the front propagation (FP) level set algorithm of Malladi, Sethian, and Vemuri and compare it with the fuzzy connectedness family of algorithms. In particular, we prove that the FP algorithm is weakly model-equivalent with the absolute fuzzy connectedness algorithm of Udupa and Samarasekera used with gradient based affinity. Experimental evidence of this equivalence is also provided. The presented theoretical framework can be used to analyze any arbitrary segmentation algorithm. This line of investigation is a subject of our forthcoming work.

Popular semi-supervised image segmentation networks suf-fer from two problems: firstly, supervision is only performed on the last layer of the decoder, resulting in the network's weak generalization ability; secondly, the geometry shape constraints of targets are frequently disregarded in these net-works, leading to poor segmentation results. To address these issues, we propose a novel shape-guided dual consistency semi-supervised learning framework for 3D medical image segmentation. The proposed framework makes two contri-butions. Initially, we introduce a shape constraint to learn the shape representation, which converts the difference be-tween two networks into an unsupervised loss and lets the model learn the boundary information of targets. Addition-ally, we develop a deep-supervised knowledge transfer strat-egy that improves the generalization ability of the network without increasing extra computation costs. Experiments demonstrate that the proposed framework outperforms state-of-the-art semi-supervised methods due to the strong ability of knowledge mining on unlabeled data.

P-018: Automatic analysis of magnetic resonance imaging in multiple myeloma patients: deep-learning based pelvic bone marrow segmentation and radiomics analysis for prediction of plasma cell infiltration