Optimum Regularized Joint Registration and Segmentation Method for Medical Brain Images

In this paper, we propose a novel framework for the segmentation of noisy images by incorporating the advantages of k-means clustering and distance regularized level set evolution (DRLSE). Level set methods and active contour models (ACMs) plays a vital role in the applications of image processing, robot vision, object recognition and computer vision. DRLSE model has recently become a powerful technique for image segmentation. DRLSE model eliminates the re-initialization problem in conventional level set method. DRLSE has been applied successfully into some fields like medical imaging, remote sensing and computer vision. However when it is applied to noisy images, It leads to significant drawbacks (number of iterations and computational time is increased). In order to avoid disadvantages of conventional DRLSE, we introduce a method to combine the median filtering, k-means clustering and DRLSE model. Firstly a noise free image is extracted by median filtering; then k-means clustering is applied to denoised image. The last stage is that the DRLSE model is applied for the extraction of object boundaries with pre segmentation process. The accuracy and the efficiency of the algorithm can be described on various noisy magnetic resonance (MR) brain images. The experiments show that our proposed method is more effective for noisy images.

The signal processing community is increasingly interested in using information theoretic concepts to build signal processing algorithms for a variety of applications. A general theory on how to apply the mathematical concepts of information theory to the field of signal processing would therefore be of great interest. This is one of the main goals of this thesis, namely to introduce a mathematical framework for information theoretic signal and image processing. The framework is based on stochastic processes for information transmission and on the error probabilities associated to these transmissions. Within the developed model, the stochastic processes account for the signal processing tasks within probability space, and the error probabilities are the optimization functions that drive the algorithms towards the signal processing objectives. The resulting conceptual framework allows us to directly apply a large number of information theoretic concepts and formulae to signal processing, including lower error bounds for the error probabilities or concepts from rate-distortion theory. In order to illustrate the theoretic framework, we show that several existing information theoretic signal processing algorithms implicitly fit our general model. This allows us to study interesting relationships between several algorithms. More importantly, we also apply the theory to three important target applications, namely multi-modal medical image registration, audio-video joint processing, and non-parametric, non-supervised classification. The first two applications are particular examples of the general concept of multi-modal feature extraction. Multi-modal feature extraction aims to determine those features in a pair of multi-modal signals that carry maximal mutual redundancy. This means that from the feature space representation of one signal we can predict the feature space representation of the second signal with low probability of error. After describing the mathematical basis, we illustrate the algorithm with examples of multi-modal medical image registration, where the algorithm adaptively extracts those features in the initial datasets which best perform the registration task. Again, this is done by determining those features which carry maximal mutual redundancy and therefore define optimally spatial registration. We also apply the model to audio-video signals to predict the localization of a speaker in a video scene from its corresponding speech signal. The resulting algorithms illustrate that the existence of features with large mutual redundancy in multi-modal signals can be used to improve multi-modal signal processing. Furthermore the general theory enables the construction of a wide range of completely new applications. Another illustrative example of the general information theoretic signal processing framework consists of information theoretic classification. Even though the basic model for multi-modal feature extraction and classification is identical, the final mathematical expressions are different and complementary. This allows us to make very interesting analogies between these two distinct applications. In particular, it is interesting to see that in analogy to registration, also classification algorithms aim to minimize error probabilities. The entirely probabilistic nature of the classification framework allows us to add a hidden Markov random field to the algorithms, resulting in the promising concept of non-parametric hidden Markov models. The classification algorithms are validated on synthetic and natural data. For instance, we apply the non-parametric hidden Markov model to the segmentation of medical images and obtain promising results in comparison to the state-of-the-art in this field. In conclusion, the experimental results show that the introduced mathematical framework leads to interesting generalizations of existing signal processing tasks and to promising results for several newly derived signal processing algorithms.

We introduce an automated pathology classification system for medical volumetric brain image slices. Existing work often relies on handcrafted features extracted from automatic image segmentation. This is not only a challenging and time-consuming process, but it may also limit the adaptability and robustness of the system. We propose a novel approach to combine sparse Gabor-feature based classifiers in an ensemble classification framework. The unsupervised nature of this non-parametric technique can significantly reduce the time and effort for system calibration. In particular, classification of medical images in this framework does not rely on segmentation, nor semantic-based or annotation-based feature selection. Our experiments show very promising results in classifying computer tomography image slices into pathological classes for traumatic brain injury patients.

Segmentation is an important step in medical image analysis. This process is crucial but challenging due to inhomogeneneity in intensity of images. In addition, the images are often corrupted by noise and with contrast edges. There are some approaches aiming to cope with this kind of images such as: region growing, region competition, watershed segmentation, global thresholding, and active contour methods. Among them, active contour methods, especially level set-based active contour is widely used for image segmentation by their advantageous properties such as topology adaptability, and robustness to initialization. In this paper, we present and demonstrate the effectiveness of some recently active contour models for segmenting medical images with inhomogeneity in intensity. Among these techniques, the local binary fitting based model is validated as a promising method for medical image segmentation.

Introduction: This paper proposed a kind of segmentation method for medical CBCT image in liver organ based on Bayesian network. Methods: Taking CBCT medical image of liver organ as a focus of medical image segmentation and to segment the area we are interested in with noise elimination and image enhancement. In order to show multiple image information including the liver organ CBCT image color, texture, shape and other features, image information can be extracted, and the extracted image features can be classified from the perspective of data mining by Bayesian network. Results: The method ensures that the target points of the liver organ CBCT image are clearly visible, which is not only suitable for the normal image registration, but also for the disordered image registration. Bayesian network method has good organization ability to distinguish pixels with similar gray level belonging to different tissues in the image, and map them back to the image space, so that tissue extraction from liver organ CBCT images has a good effect. Conclusion: The CBCT images are analysed based on medical image database to better achieve the required characteristics in data mining, extraction of non-rigid registration and image segmentation technology. And the result shows that this kind of method based on Bayesian network is a good theoretical method that can achieve expected outcome and the accuracy rate is good with high practical application.

Joint segmentation and registration of images is a focused area of research nowadays. Jointly segmenting and registering noisy images and images having weak boundaries/intensity inhomogeneity is a challenging task. In medical image processing, joint segmentation and registration are essential methods that aid in distinguishing structures and aligning images for precise diagnosis and therapy. However, these methods encounter challenges, such as computational complexity and sensitivity to variations in image quality, which may reduce their effectiveness in real-world applications. Another major issue is still attaining effective joint segmentation and registration in the presence of artifacts or anatomical deformations. In this paper, a new nonparametric joint model is proposed for the segmentation and registration of multi-modality images having weak boundaries/noise. For segmentation purposes, the model will be utilizing local binary fitting data term and for registration, it is utilizing conditional mutual information. For regularization of the model, we are using linear curvature. The new proposed model is more efficient to segmenting and registering multi-modality images having intensity inhomogeneity, noise and/or weak boundaries. The proposed model is also tested on the images obtained from the freely available CHOAS dataset and compare the results of the proposed model with the other existing models using statistical measures such as the Jaccard similarity index, relative reduction, Dice similarity coefficient and Hausdorff distance. It can be seen that the proposed model outperforms the other existing models in terms of quantitatively and qualitatively.

The rapid advancements in medical imaging technologies have significantly enhanced diagnostic accuracy and clinical decision-making in modern healthcare. Image segmentation and deep learning have emerged as transformative tools among these advancements. This article explores the pivotal role of image segmentation and deep learning in medical imaging, detailing their methodologies, applications, challenges, and future directions. Deep learning, particularly Convolutional Neural Networks (CNNs), has revolutionized medical imaging by automating the analysis of complex datasets and improving diagnostic precision. Image segmentation, a fundamental component of medical imaging, allows for delineating specific structures such as organs, tissues, and pathological regions. Together, these technologies have been applied in diverse fields, including oncology, cardiology, neurology, and ophthalmology, enabling applications such as tumor detection, organ segmentation, disease progression monitoring, and treatment planning. However, despite its transformative potential, the integration of deep learning into medical imaging faces several challenges. These include data scarcity, privacy concerns, interpretability issues, and regulatory hurdles. The article discusses various strategies to address these challenges, such as data augmentation, transfer learning, and the development of explainable AI models to ensure transparency and trustworthiness. Evaluation metrics, such as accuracy, sensitivity, specificity, and Dice Similarity Coefficient (DSC), are essential for assessing model performance. Rigorous clinical validation and regulatory approval are crucial to integrating deep learning systems into clinical workflows effectively. Looking ahead, the future of deep learning in medical imaging holds immense promise. Innovations like multimodal imaging, personalized medicine, and AI-driven automation are set to further revolutionize the field, enhancing the efficiency and accuracy of diagnostics. Collaborative efforts between clinicians, researchers, and AI developers will play a vital role in overcoming current limitations and driving progress. This article concludes by emphasizing the transformative potential of deep learning and image segmentation in medical imaging, highlighting their ability to improve diagnostic accuracy, streamline clinical workflows, and ultimately, enhance patient care. By addressing current challenges and continuing to innovate, these technologies are poised to redefine the landscape of medical diagnostics and treatment in the years to come.

Over the last two decades medical image processing has become a fundamental tool in medicine, and brain imaging is a paradigm thereof. The fast development of the imaging acquisition techniques allows medical staff to dispose of a variety of data coming from different imaging modalities. However, the analysis of such amount of data based on visual inspection is very difficult and highly time consuming. Often, the information contained in a medical image cannot be entirely seen by a human eye and vice-versa, computers do not have human common sense or the experience acquired by medical experts. Therefore, it is desirable to combine both medical experts and computers in an optimal trade-off to improve the outcome of the wide range of applications where medical imaging is nowadays applied. Among these applications we can mention diagnosis, surgical planning and intra-operative surgical navigation. Image registration is one of the most popular image processing techniques used in clinical environments. It consists of bringing two or more images into a single spatial representation, i.e. finding the optimal geometric transformation between the data. Image registration overcomes the difficulties encountered by clinicians to fuse images mentally since it enables to integrate different images into one representation. The applications of image registration in medicine are numerous and can be grouped in clinical, related to detection and diagnosis, and surgical. Some of these applications are: preprocedural planning and simulation, interventional radiology, diagnostic radiology, minimally invasive procedures, radiation therapy, intraoperative navigation, robot-assisted interventions, etc. During the decade of the 90s a large number of registration algorithms were proposed, linked to a variety of medical applications. Nowadays, rigid registration is considered to be a well-covered domain with efficient solutions for the most common applications. Current research mostly focuses on nonrigid registration methods. However, the complex framework of nonrigid registration makes it a complex problem where there is not a universal solution. This complex framework includes a number of components that interact: the dimensionality of the data involved, the feature space to base the registration on, the kind and domain of the transformation model, the modalities of the data and the subjects involved, the user interaction, the similarity metric to assess the alignment quantitatively, the search space where the optimal solution has to be found, and the search strategy including optimization of the objective function and implementation details. We can summarize the motivation of this thesis in the following sentence: Validation of nonrigid registration algorithms is a very difficult task and rather an application-dependent problem. Therefore, this dissertation is structured to face the problem of brain image registration in three closely correlated parts: algorithms, applications and validation. In the algorithmic context, we propose a control point based nonrigid registration algorithm which aims to improve the performance of classical point based algorithms. In the framework of the implementation of the algorithm we develop a control point detector based on information theory tools and a transformation model based on a type of radial basis functions specially suited for interpolation of scattered and nonuniform distributed data samples. The algorithm is evaluated for typical inter-subject monomodal and multimodal brain image registration. In the context of clinical applications we face a neurosurgical application: the subthalamic nucleus targeting for deep brain stimulation in Parkinson's disease surgery. The extensive study covers from state-of-the-art targeting procedures to automatic targeting methods through different registration algorithms. Moreover, we analyze the influence of surrounding anatomical features on the target location. We also study the feasibility of an atlas of landmarks aiming to improve the targeting accuracy and at the same time to reduce both the computational cost and the preprocessing needed compared to the other automatic targeting methods proposed. All the proposed methods and techniques are statistically cross-validated against state-of-the-art techniques and expert's targeting variability through an application-adapted validation scheme. The results show that automatic subthalamic nucleus localization is possible and as accurate as the methods currently used. We also provide valuable conclusions about the anatomical structures that must be used to infer more accurate targets. In the context of validation of brain image registration, we develop a general (non application-oriented) validation scheme that provides an independent and high dimensional means of assessing the quality of the alignment given by a registration algorithm. This procedure is applied to structural magnetic resonance images and is based on the information carried by the diffusion tensor images. It provides an error measure per voxel allowing an independent evaluation for different regions. Almost 800 registered images are analyzed to provide with strength the conclusions derived from the statistical analysis.

Traditional medical image segmentation methods have problems such as low segmentation accuracy and low adaptive ability. Therefore, many scholars have proposed a medical image segmentation method based on deep learning, which has achieved good results in the field of medical image segmentation. However, this type of method has the following problems in the application process: (1) Medical image segmentation target boundary positioning problem. Constrained by factors such as medical image contrast, heterogeneity, and boundary resolution, existing convolution models still cannot accurately locate boundaries. (2) Deep adaptability of deep learning network structure to medical images. Because medical images have more distinct and different feature information than natural images, the current deep learning-based medical segmentation methods have not fully considered this feature. In view of this, this paper proposes a multi-level boundary-aware RUNet segmentation model. The network structure consists of a U-Net-based segmentation network and a multi-level boundary detection network. It can solve the problem of boundary positioning. At the same time, in order to solve the problem of poor adaptability of deep learning network structures to medical images, this paper proposes to introduce a new interactive self-attention module into deep learning models. It can make the feature map get global information, and realize the effective extraction of medical image feature information. It solves the problem of weak matching between the deep learning network structure and medical images. Based on the above ideas, this paper proposes an image segmentation algorithm based on a multi-layer boundary perception-self-attention mechanism deep learning model. This method and other mainstream segmentation algorithms are used to perform experiments on related medical databases. The results show that the proposed method not only improves the segmentation effect significantly compared with traditional machine learning methods, but also improves it to a certain extent compared with other deep learning methods.

A Basic Model for IVUS Image Simulation.- Quantitative Functional Imaging with Positron Emission Tomography.- Advances in Magnetic Resonance Angiography and Physical Principles.- Recent Advances in the Level Set Method - Shape from Shading Models.- Wavelets in Medical Image Processing - Improving the Initialization, Convergence, and Memory Utilization for Defomable Models.- Level Set Segmentation of Biological Volume Database.- Advanced Segmentation (Level Set) Techniques.- A Regional-aided Color Geometric Snake.- Co-Volume Level Set Method in Subjective Surface Based Medical Image Segmentation.- Model-Based Brain Tissue Classification.- Supervised Texture Classification for Intravascular Tissue Characterization.- Medical Image Segmentation: Methods and Applications in Functional Imaging.- Automatic Segmentation of Pancreatic Tumors in Computed Tomography.- Computerized Analysis and Vasodilation Parameterization in Flow-Mediated Dilation Tests from Ultrasonic Image Sequences.- Statistical and Adaptive Approaches for Optimal Segmentation in Medical Images.- Automatic Analysis of Color Fundus Photographs and its Application to the Diagnosis of Diabetic Retinopathy.- Segmentation Issues in Carotid Artery Atherosclerotic Plague Analysis with MRI.- Accurate Lumen Identification, Detection, and Quantification in MR Plague Volumes.- Hessian-based Multiscale Enhancement, Description, and Quantification of Second-Order 3D Local Structures from Medical Volume Data.- A Knowledge-Based Scheme for Digital Mammography - Simultaneous Fuzzy Segmentation of Medical Images.- Computer Aided Diagnosis of Mammographic Calcification Clusters: Impact of Segmentation.- Computer Supported Segmentation of Radiological Data.- Medical Image Registration: Theory Algorithms, and Case Studies.- State of the Art of Level Set Methods in Segmentation and Registration of Medical Imaging Modalities.- Three-Dimensional Rigid and Non-Rigid Image Restriction for the Pelvis and Prostate.- Stereo and Temporal Retinal Image Registration by Mutual Information Maximization.- Quantification of Brain Aneurysm Dimensions from CTA for Surgical Planning of Coiling Intervention.- Inverse Consistent Image Registration.- A Computer-Aided Design System for Segmentation of Volumetric Images.- Inter-subject Non-Rigid Registration: an Overview with Classification and the Romeo Algorithm.- Elastic Registration for Biomedical Applications.- Cross-entropy, reversed cross-entropy, and symmetric divergence similarity measures for 3D image registration: a comparative study.- Quo Vadis, Atlas-Based Segmentation?.- Index.

A Basic Model for IVUS Image Simulation.- Quantitative Functional Imaging with Positron Emission Tomography.- Advances in Magnetic Resonance Angiography and Physical Principles.- Recent Advances in the Level Set Method - Shape from Shading Models.- Wavelets in Medical Image Processing - Improving the Initialization, Convergence, and Memory Utilization for Defomable Models.- Level Set Segmentation of Biological Volume Database.- Advanced Segmentation (Level Set) Techniques.- A Regional-aided Color Geometric Snake.- Co-Volume Level Set Method in Subjective Surface Based Medical Image Segmentation.- Model-Based Brain Tissue Classification.- Supervised Texture Classification for Intravascular Tissue Characterization.- Medical Image Segmentation: Methods and Applications in Functional Imaging.- Automatic Segmentation of Pancreatic Tumors in Computed Tomography.- Computerized Analysis and Vasodilation Parameterization in Flow-Mediated Dilation Tests from Ultrasonic Image Sequences.- Statistical and Adaptive Approaches for Optimal Segmentation in Medical Images.- Automatic Analysis of Color Fundus Photographs and its Application to the Diagnosis of Diabetic Retinopathy.- Segmentation Issues in Carotid Artery Atherosclerotic Plague Analysis with MRI.- Accurate Lumen Identification, Detection, and Quantification in MR Plague Volumes.- Hessian-based Multiscale Enhancement, Description, and Quantification of Second-Order 3D Local Structures from Medical Volume Data.- A Knowledge-Based Scheme for Digital Mammography - Simultaneous Fuzzy Segmentation of Medical Images.- Computer Aided Diagnosis of Mammographic Calcification Clusters: Impact of Segmentation.- Computer Supported Segmentation of Radiological Data.- Medical Image Registration: Theory Algorithms, and Case Studies.- State of the Art of Level Set Methods in Segmentation and Registration of Medical Imaging Modalities.- Three-Dimensional Rigid and Non-Rigid Image Restriction for the Pelvis and Prostate.- Stereo and Temporal Retinal Image Registration by Mutual Information Maximization.- Quantification of Brain Aneurysm Dimensions from CTA for Surgical Planning of Coiling Intervention.- Inverse Consistent Image Registration.- A Computer-Aided Design System for Segmentation of Volumetric Images.- Inter-subject Non-Rigid Registration: an Overview with Classification and the Romeo Algorithm.- Elastic Registration for Biomedical Applications.- Cross-entropy, reversed cross-entropy, and symmetric divergence similarity measures for 3D image registration: a comparative study.- Quo Vadis, Atlas-Based Segmentation?.- Index.

Vision information processing (VIP) is the important supports of image processing. Currently, VIP has become as a leader direction in remote sense image processing (which mostly serves the government and military) and in medical Image processing (which widely serves a great numbers of patients). Medical imaging and medical image analysis techniques are the hotspots of the biomedical engineering. On one hand, different from optical imaging, modern medical imaging such as CT, MR and PET have the very complex imaging mechanisms with deep mathematic fundamental and are entirely different with each other. Advanced and novel precise techniques in medical imagine are also needed, such as design of various filters, calibration techniques for different artifacts, fast imaging methods and low dose CT reconstruction. New important applications of medical imaging are still in progress with high speed, which include special imaging technique to some diseases, multi-functional imaging equipments and special imaging devices for brain or hand. On the other hand, medical image analysis such as image segmentation and image registration as the basic medical image processing still require some novel techniques to make it more effectively. Fuzziness of physiology estimation, stochastic behavior of imaging process, and ill condition behavior of mathematic model may be the dispute problems for a long time. For more convenient, we are to quite our recent research results to illustrate above the hotspots.

To cope with a variety of clinical applications, research in medical image processing has led to a large spectrum of segmentation techniques that extract anatomical structures from volumetric data acquired with 3D imaging modalities. Despite continuing advances in mathematical models for automatic segmentation, many medical practitioners still rely on 2D manual delineation, due to the lack of intuitive semi-automatic tools in 3D. In this thesis, we propose a methodology and associated numerical schemes enabling the development of 3D image segmentation tools that are reliable, fast and interactive. These properties are key factors for clinical acceptance. Our approach derives from the framework of variational methods: segmentation is obtained by solving an optimization problem that translates the expected properties of target objects in mathematical terms. Such variational methods involve three essential components that constitute our main research axes: an objective criterion, a shape representation and an optional set of constraints. As objective criterion, we propose a unified formulation that extends existing homogeneity measures in order to model the spatial variations of statistical properties that are frequently encountered in medical images, without compromising efficiency. Within this formulation, we explore several shape representations based on implicit surfaces with the objective to cover a broad range of typical anatomical structures. Firstly, to model tubular shapes in vascular imaging, we introduce convolution surfaces in the variational context of image segmentation. Secondly, compact shapes such as lesions are described with a new representation that generalizes Radial Basis Functions with non-Euclidean distances, which enables the design of basis functions that naturally align with salient image features. Finally, we estimate geometric non-rigid deformations of prior templates to recover structures that have a predictable shape such as whole organs. Interactivity is ensured by restricting admissible solutions with additional constraints. Translating user input into constraints on the sign of the implicit representation at prescribed points in the image leads us to consider inequality-constrained optimization.

In this paper, we propose an approach to detection and segmentation of liver tumors in noisy computed topography (CT) images. Image segmentation plays crucial role in medical image processing applications. Noise is quite common in medical images. It occurs while acquisition and transmission of images. The essential goal of this framework is to identify liver cancer by segmenting liver tumors from noisy CT scan images. Liver segmentation is difficult task in medical applications because inter-patient variability in size, shape and disease. In general CT scanning is used to inspect liver cancer. In this research work, the liver tumors are detected by the medical images in three stages, pre-processing stage, processing stage and detection stage. First in pre-processing stage, median filter is used to remove the noise from CT image, and then the denoised image is segmented by fuzzy c-means clustering (FCM) algorithm. Finally in the detection stage distance regularized level set evolution (DRLSE) is used to extract tumor boundaries. This algorithm is very much useful for identifying hepatocellular carcinoma (liver cancer). Experimental results on various noisy CT scan images show that the proposed method is efficient for extracting hepatic tumors from liver.

In the field of image analysis, geometric modeling and simulation of real-world problems, spline-based methods are powerful tools to develop smooth and accurate representation of the solution. In this dissertation, we propose several methods to improve the efficiency andaccuracy of B-spline based methods for different applications such as image registration, image segmentation and modeling neuron growth. Image registration is the process of finding accurate spatial correspondence between two or more images. This field has several applications such as feature tracking and fusion of images taken at different perspectives, time frames or even modalities. Image segmentation is the process of detecting importantfeatures from images. The image is partitioned into multiple labeled regions denoting each object of interest.The development of a B-spline based image registration framework that can capture large scale deformations through local refinement is carried out in order to achieve higher accuracy in less computational time. We present an efficient approach for Finite Element Method (FEM)-based nonrigid image registration, in which the spatial transformation is constructed using truncated hierarchical B-splines (THB-splines). Instead of uniform subdivision, we propose an adaptive local refinement scheme to only refine the areas of large change in deformation of the image. By incorporating the key advantages of THB-splinebasis functions such as linear independence, partition of unity and reduced overlap into the FEM-based framework, we improve the matrix sparsity and computational efficiency.The performance of the proposed method is demonstrated on 2D synthetic and medical images. We extend the algorithm to perform 3D nonrigid image registration suitable for large deformation and topology change. Control points are dynamically updated without constructing large matrices as in the finite element method. The proposed method isdemonstrated on 3D synthetic and medical images to show robustness with respect to topology change as compared to other image registration methods. In order to combine segmentation and registration in one framework, we present a novel approach for joint image segmentation and nonrigid registration using bidirectional composition to update the spatial transformation function. Unlike previous approaches,the implicit level set function defining the segmentation contour and the spatial transformationfunction are both represented using B-splines. This joint level set framework uses a variational form of an atlas-based segmentation together with large deformation basednonrigid registration. The improvement in the description of the segmentation result using B-splines leads to better accuracy of both the image segmentation and registration process. We propose a novel automatic neuron segmentation framework using a B-spline based activecontour deformation model with hyperelastic regularization and automatic initialization. This boundary-extraction based algorithm utilizes cubic B-splines to deform active contoursto match the neuron cell surface accurately. Using adaptive local refinement, finer level deformation of the active contour is captured using THB-splines in a multiresolution manner.By introducing hyperelastic regularization, we allow large nonlinear deformations of the active contours. Unlike other existing methods which represent neuron boundary aspiecewise constant function, we provide a more accurate and smooth representation of the neuron geometry.Lastly, we have focused on developing realistic computational models for modeling different stages of neuron growth using phase field method. The multi-resolution phase field method utilizes THB-splines to evaluate the gradient of the phase field variable andimprove smoothness. The stages modeled include lamellipodia formation, initial neurite outgrowth, axon differentiation and dendritic branching. Neuron growth is driven by the extracellular culture medium and intracellular transport of tubulin. Through comparison withexperimental observations, we can demonstrate a good reproduction of neuron morphologies at different stages of growth and allow extension towards formation of neurite networks.