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Background: In hypoplastic left heart syndrome, tricuspid regurgitation (TR) is associated with circulatory failure and death. We hypothesized that the tricuspid valve (TV) structure of patients with hypoplastic left heart syndrome with a Fontan circulation and moderate or greater TR differs from those with mild or less TR, and that right ventricle volume is associated with TV structure and dysfunction. Methods: TV of 100 patients with hypoplastic left heart syndrome and a Fontan circulation were modeled using transthoracic 3-dimensional echocardiograms and custom software in SlicerHeart. Associations of TV structure to TR grade and right ventricle function and volume were investigated. Shape parameterization and analysis was used to calculate the mean shape of the TV leaflets, their principal modes of variation, and to characterize associations of TV leaflet shape to TR. Results: In univariate modeling, patients with moderate or greater TR had larger TV annular diameters and area, greater annular distance between the anteroseptal commissure and anteroposterior commissure, greater leaflet billow volume, and more laterally directed anterior papillary muscle angles compared to valves with mild or less TR (all P P P Conclusions: Moderate or greater TR in patients with hypoplastic left heart syndrome with a Fontan circulation is associated with greater leaflet billow volume, a more laterally directed anterior papillary muscle angle, and greater annular distance between the anteroseptal commissure and anteroposterior commissure. However, there is significant heterogeneity of structure in the TV leaflets in regurgitant valves. Given this variability, an image-informed patient-specific approach to surgical planning may be needed to achieve optimal outcomes in this vulnerable and challenging population.

Surgery for nasal airway obstruction (NAO) has a high failure rate, with up to 50% of patients reporting persistent symptoms postoperatively. Virtual surgery planning has the potential to improve surgical outcomes, but current manual methods are too labor-intensive to be adopted on a large scale. This manuscript introduces an automatic atlas-based approach for performing virtual septoplasties. A cohort of 47 healthy subjects and 26 NAO patients was investigated. An atlas of healthy nasal geometry was constructed. The automatic virtual septoplasty method consists of a multi-stage registration approach to fit the atlas to a target NAO patient, automatically segment the patient’s septum and airway, and deform the patient image to have a non-deviated septum. Our automatic virtual septoplasty method straightened the septum successfully in 18 out of 26 NAO patients (69% of cases). In these cases, the ratio of the higher to the lower airspace cross-sectional areas in the left and right nasal cavities improved from 1.47 ± 0.45 to 1.16 ± 0.33 in the region surrounding the septal deviation, showing that the nasal airway became more symmetric after virtual septoplasty. This automated virtual septoplasty technique has the potential to greatly reduce the effort required to perform computational fluid dynamics (CFD) analysis of nasal airflow for NAO surgical planning. Future studies are needed to investigate if virtual surgery planning using this method is predictive of subjective symptoms in NAO patients after septoplasty.

INTRODUCTION In the surgical fixation of fractures, proper biomechanical stability is key in preventing clinical complications including poor fracture healing, residual deformity, loss of fixation, or implant failure. Stability is largely influenced by treatment decisions made by the surgeon. The interplay of surgeon-controlled variables and their effect on the three-dimensional (3D) biomechanics of a fracture fixation construct are often not intuitive, and current training methods do not facilitate a deep understanding of these interactions. METHODS A simulation software interface, FracSim, was developed. FracSim is built on a large precomputed library of finite element simulations. The software allows a surgeon to make adjustments to a virtual fracture fixation construct/weight-bearing plan and immediately visualize how these changes affect 3D biomechanics, including implant stress and fracture gap strain, important for clinical success. Twenty-one orthopaedic residents completed an instructor-led educational session with FracSim focused on bridge plating. Subjects completed pretests and posttests of knowledge of biomechanical concepts and a questionnaire. RESULTS Subjects scored a mean of 5.6/10 on the pretest of biomechanical knowledge. Senior residents scored better than junior residents (P = 0.04). After the educational session with FracSim, residents improved their test scores to a mean of 8.0/10, with a significant improvement (P < 0.001). Questionnaire scores indicated that subjects believed that FracSim had realistic implants, constructs, and motions and that training with FracSim was purposeful, desirable, efficient, fun, and useful for enhancing the understanding of fracture fixation biomechanics. DISCUSSION This new type of simulation software enables interactive visualization of 3D fracture fixation biomechanics. Limitations of this study include lack of a control group undergoing traditional education and lack of a delayed posttest to assess retention. FracSim may provide an effective and engaging way to promote a deeper understanding of biomechanical concepts in the orthopaedic learner.

Microfractures (cracks) are the third most common cause of tooth loss in industrialized countries. If they are not detected early, they continue to progress until the tooth is lost. Cone beam computed tomography (CBCT) has been used to detect microfractures, but has had very limited success. We propose an algorithm to detect cracked teeth that pairs high resolution (hr) CBCT scans with advanced image analysis and machine learning. First, microfractures were simulated in extracted human teeth (n=22). hr-CBCT and microCT scans of the fractured and control teeth (n=14) were obtained. Wavelet pyramid construction was used to generate a phase image of the Fourier transformed scan which were fed to a U-Net deep learning architecture that localizes the orientation and extent of the crack which yields slice-wise probability maps that indicate the presence of microfractures. We then examine the ratio of high-probability voxels to total tooth volume to determine the likelihood of cracks per tooth. In microCT and hr-CBCT scans, fractured teeth have higher numbers of such voxels compared to control teeth. The proposed analytical framework provides a novel way to quantify the structural breakdown of teeth, that was not possible before. Future work will expand our machine learning framework to 3D volumes, improve our feature extraction in hr-CBCT and clinically validate this model. Early detection of microfractures will lead to more appropriate treatment and longer tooth retention.

Repair of complete atrioventricular canal (CAVC) is often complicated by residual left atrioventricular valve regurgitation. The structure of the mitral and tricuspid valves in biventricular hearts has previously been shown to be associated with valve dysfunction. However, the three-dimensional (3D) structure of the entire unrepaired CAVC valve has not been quantified. Understanding the 3D structure of the CAVC may inform optimized repair.Novel open-source work flows were created in SlicerHeart for the modeling and quantification of CAVC valves on the basis of 3D echocardiographic images. These methods were applied to model the annulus, leaflets, and papillary muscle (PM) structure of 35 patients (29 with trisomy 21) with CAVC using transthoracic 3D echocardiography. The mean leaflet and annular shapes were calculated and visualized using shape analysis. Metrics of the complete native CAVC valve structure were compared with those of normal mitral valves using the Mann-Whitney U test. Associations between CAVC structure and atrioventricular valve regurgitation were analyzed.CAVC leaflet metrics varied throughout systole. Compared with normal mitral valves, the left CAVC PMs were more acutely angled in relation to the annular plane (P .001). In addition, the anterolateral PM was laterally and inferiorly rotated in CAVC, while the posteromedial PM was more superiorly and laterally rotated, relative to normal mitral valves (P .001). Lower native CAVC atrioventricular valve annular height and annular height-to-valve width ratio before repair were both associated with moderate or greater left atrioventricular valve regurgitation after repair (P .01).It is feasible to model and quantify 3D CAVC structure using 3D echocardiographic images. The results demonstrate significant variation in CAVC structure across the cohort and differences in annular, leaflet, and PM structure compared with the mitral valve. These tools may be used in future studies to catalyze future research intended to identify structural associations of valve dysfunction and to optimize repair in this vulnerable and complex population.

Hypoplastic left heart syndrome (HLHS) is a congenital heart disease characterized by incomplete development of the left heart. Children with HLHS undergo a series of operations which result in the tricuspid valve (TV) becoming the only functional atrioventricular valve. Some of those patients develop tricuspid regurgitation which is associated with heart failure and death and necessitates further surgical intervention. Repair of the regurgitant TV, and understanding the connections between structure and function of this valve remains extremely challenging. Adult cardiac populations have used 3D echocardiography (3DE) combined with computational modeling to better understand cardiac conditions affecting the TV. However, these structure-function analyses rely on simplistic point-based techniques that do not capture the leaflet surface in detail, nor do they allow robust comparison of shapes across groups. We propose using statistical shape modeling and analysis of the TV using Spherical Harmonic Representation Point Distribution Models (SPHARM-PDM) in order to generate a reproducible representation, which in turn enables high dimensional low sample size statistical analysis techniques such as principal component analysis and distance weighted discrimination. Our initial results suggest that visualization of the differences in regurgitant vs. non-regurgitant valves can precisely locate populational structural differences as well as how an individual regurgitant valve differs from the mean shape of functional valves. We believe that these results will support the creation of modern image-based modeling tools, and ultimately increase the understanding of the relationship between valve structure and function needed to inform and improve surgical planning in HLHS.

Surgery for nasal airway obstruction (NAO) has a high failure rate, with up to 50% of patients reporting persistent symptoms postoperatively. Virtual surgery planning has the potential to improve surgical outcomes, but current manual methods are too labor-intensive to be adopted on a large scale. This manuscript introduces an automatic atlas-based approach for performing virtual septoplasties.A cohort of 47 healthy subjects and 26 NAO patients was investigated. An atlas of healthy nasal geometry was constructed. The automatic virtual septoplasty method consists of a multi-stage registration approach to fit the atlas to a target NAO patient, automatically segment the patient's septum and airway, and deform the patient image to have a non-deviated septum.Our automatic virtual septoplasty method straightened the septum successfully in 18 out of 26 NAO patients (69% of cases). In these cases, the ratio of the higher to the lower airspace cross-sectional areas in the left and right nasal cavities improved from 1.47 ± 0.45 to 1.16 ± 0.33 in the region surrounding the septal deviation, showing that the nasal airway became more symmetric after virtual septoplasty.This automated virtual septoplasty technique has the potential to greatly reduce the effort required to perform computational fluid dynamics (CFD) analysis of nasal airflow for NAO surgical planning. Future studies are needed to investigate if virtual surgery planning using this method is predictive of subjective symptoms in NAO patients after septoplasty.

The Pulse Physiology Platform is an open-source software application designed to enable accurate and consistent, real-time physiologic simulations for improved medical training and clinical decision-making tools. The platform includes a physiology engine comprised of well-validated lumped-parameter models, differential equations representing feedback mechanisms, and a pharmacokinetic/pharmacodynamic model. The platform also includes a common data model for standard model and data definitions and a common software interface for engine control and robust physics-based circuit and transport solvers. The Pulse Platform has been incorporated into a number of commercial, research, and academic tools for medical simulation. Significance: The Pulse Platform is an innovative, well-validated, open-source tool for medical modeling and simulation in the training and clinical decision-making field.

Shape analysis is an important and powerful tool in a wide variety of medical applications. Many shape analysis techniques require shape representations which are in correspondence. Unfortunately, popular techniques for generating shape representations do not handle objects with complex geometry or topology well, and those that do are not typically readily available for non-expert users. We describe a method for generating correspondences across a population of objects using a given template. We also describe its implementation and distribution via SlicerSALT, an open-source platform for making powerful shape analysis techniques more widely available and usable. Finally, we show results of this implementation on mouse femur data.

Skeletal models that are structurally medial provide effective object representations. This is because they include not only locations but also boundary directions and object widths. We present a skeletal object representation that we call “quasimedial” because geometric properties associated with Blum's [1] medial axis are relaxed to allow the skeleton to have a pre-specified amount of branching and thus to support statistical analysis. We call this form of object representation the s-rep. We explain how such models can be automatically determined from object boundary data in a way that a) avoids boundary noise, b) implies a boundary that closely fits the input boundary, and c) well recognizes shape correspondences across cases. We also explain how to use Riemannian geometry to estimate probability distributions from a sample of s-reps and to find ways to classify s-reps between two categories as trained from s-reps in each class. Finally, we describe various evidence that shows the relative strengths of s-reps vs. other object representations; we also discuss shortcomings of s-reps.

ITK-SNAP is an interactive software tool for manual and semi-automatic segmentation of 3D medical images. This paper summarizes major new features added to ITK-SNAP over the last decade. The main focus of the paper is on new features that support semi-automatic segmentation of multi-modality imaging datasets, such as MRI scans acquired using different contrast mechanisms (e.g., T1, T2, FLAIR). The new functionality uses decision forest classifiers trained interactively by the user to transform multiple input image volumes into a foreground/background probability map; this map is then input as the data term to the active contour evolution algorithm, which yields regularized surface representations of the segmented objects of interest. The new functionality is evaluated in the context of high-grade and low-grade glioma segmentation by three expert neuroradiogists and a non-expert on a reference dataset from the MICCAI 2013 Multi-Modal Brain Tumor Segmentation Challenge (BRATS). The accuracy of semi-automatic segmentation is competitive with the top specialized brain tumor segmentation methods evaluated in the BRATS challenge, with most results obtained in ITK-SNAP being more accurate, relative to the BRATS reference manual segmentation, than the second-best performer in the BRATS challenge; and all results being more accurate than the fourth-best performer. Segmentation time is reduced over manual segmentation by 2.5 and 5 times, depending on the rater. Additional experiments in interactive placenta segmentation in 3D fetal ultrasound illustrate the generalizability of the new functionality to a different problem domain.

We present a novel approach for improving the shape statistics of medical image objects by generating correspondence of skeletal points. Each object’s interior is modeled by an s-rep, i.e., by a sampled, folded, two-sided skeletal sheet with spoke vectors proceeding from the skeletal sheet to the boundary. The skeleton is divided into three parts: the up side, the down side, and the fold curve. The spokes on each part are treated separately and, using spoke interpolation, are shifted along that skeleton in each training sample so as to tighten the probability distribution on those spokes’ geometric properties while sampling the object interior regularly. As with the surface/boundary-based correspondence method of Cates et al. , entropy is used to measure both the probability distribution tightness and the sampling regularity, here of the spokes’ geometric properties. Evaluation on synthetic and real world lateral ventricle and hippocampus data sets demonstrate improvement in the performance of statistics using the resulting probability distributions. This improvement is greater than that achieved by an entropy-based correspondence method on the boundary points.

Representing an object by a skeletal structure can be powerful for statistical shape analysis if there is good correspondence of the representations within a population. Many anatomic objects have a genus-zero boundary and can be represented by a smooth unbranching skeletal structure that can be discretely approximated. We describe how to compute such a discrete skeletal structure (“d-s-rep”) for an individual 3D shape with the desired correspondence across cases. The method involves fitting a d-s-rep to an input representation of an object’s boundary. A good fit is taken to be one whose skeletally implied boundary well approximates the target surface in terms of low order geometric boundary properties: (1) positions, (2) tangent fields, (3) various curvatures. Our method involves a two-stage framework that first, roughly yet consistently fits a skeletal structure to each object and second, refines the skeletal structure such that the shape of the implied boundary well approximates that of the object. The first stage uses a stratified diffeomorphism to produce topologically non-self-overlapping, smooth and unbranching skeletal structures for each object of a population. The second stage uses loss terms that measure geometric disagreement between the skeletally implied boundary and the target boundary and avoid self-overlaps in the boundary. By minimizing the total loss, we end up with a good d-s-rep for each individual shape. We demonstrate such d-s-reps for various human brain structures. The framework is accessible and extensible by clinical users, researchers and developers as an extension of SlicerSALT, which is based on 3D Slicer.

Classifying medically imaged objects, e.g., into diseased and normal classes, has been one of the important goals in medical imaging. We propose a novel classification scheme that uses a skeletal representation to provide rich non-Euclidean geometric object properties. Our statistical method combines distance weighted discrimination (DWD) with a carefully chosen Euclideanization which takes full advantage of the geometry of the manifold on which these non-Euclidean geometric object properties (GOPs) live. Our method is evaluated via the task of classifying 3D hippocampi between schizophrenics and healthy controls. We address three central questions. 1) Does adding shape features increase discriminative power over the more standard classification based only on global volume? 2) If so, does our skeletal representation provide greater discriminative power than a conventional boundary point distribution model (PDM)? 3) Especially, is Euclideanization of non-Euclidean shape properties important in achieving high discriminative power? Measuring the capability of a method in terms of area under the receiver operator characteristic (ROC) curve, we show that our proposed method achieves strongly better classification than both the classification method based on global volume alone and the s-rep-based classification method without proper Euclideanization of non-Euclidean GOPs. We show classification using Euclideanized s-reps is also superior to classification using PDMs, whether the PDMs are first Euclideanized or not. We also show improved performance with Euclideanized boundary PDMs over non-linear boundary PDMs. This demonstrates the benefit that proper Euclideanization of non-Euclidean GOPs brings not only to s-rep-based classification but also to PDM-based classification.

Colorectal cancer is the second most common cause of cancer death in the United States, with an estimated 140,000 new cases leading to 50,000 deaths this year. The best treatment is to detect and treat the cancer before it becomes invasive and spreads. The most common form of detection is the use of optical colonoscopy in which the clinician visually inspects the surface of the colon through an endoscope to detect the presence of polyps. Studies have shown that even the best clinicians will sometimes miss polyps, especially the more subtle flat polyps, and that many cancers that develop in the years immediately following a colonoscopy likely originate from missed polyps. In this paper we describe techniques for extracting several medically-driven features from colonoscopy video that can be used to detect the presence of flat polyps. Initial quantitative and qualitative results show that each of these features on their own provide some level of discrimination and, when combined, have the potential to support robust detection of flat polyps.

SlicerSALT is an open-source platform for disseminating state-of-the-art methods for performing statistical shape analysis. These methods are developed as 3D Slicer extensions to take advantage of its powerful underlying libraries. SlicerSALT itself is a heavily customized 3D Slicer package that is designed to be easy to use for shape analysis researchers. The packaged methods include powerful techniques for creating and visualizing shape representations as well as performing various types of analysis.

A multimodal micro-computed tomography (CT) and multi-spectral structured light imaging (SLI) system is introduced and systematically analyzed to test its feasibility to aid in margin delineation during breast conserving surgery (BCS). Phantom analysis of the micro-CT yielded a signal-to-noise ratio of 34, a contrast of 1.64, and a minimum detectable resolution of 240 μm for a 1.2 min scan. The SLI system, spanning wavelengths 490 nm to 800 nm and spatial frequencies up to 1.37 [Formula: see text], was evaluated with aqueous tissue simulating phantoms having variations in particle size distribution, scatter density, and blood volume fraction. The reduced scattering coefficient, [Formula: see text] and phase function parameter, γ, were accurately recovered over all wavelengths independent of blood volume fractions from 0% to 4%, assuming a flat sample geometry perpendicular to the imaging plane. The resolution of the optical system was tested with a step phantom, from which the modulation transfer function was calculated yielding a maximum resolution of 3.78 cycles per mm. The three dimensional spatial co-registration between the CT and optical imaging space was tested and shown to be accurate within 0.7 mm. A freshly resected breast specimen, with lobular carcinoma, fibrocystic disease, and adipose, was imaged with the system. The micro-CT provided visualization of the tumor mass and its spiculations, and SLI yielded superficial quantification of light scattering parameters for the malignant and benign tissue types. These results appear to be the first demonstration of SLI combined with standard medical tomography for imaging excised tumor specimens. While further investigations are needed to determine and test the spectral, spatial, and CT features required to classify tissue, this study demonstrates the ability of multimodal CT/SLI to quantify, visualize, and spatially navigate breast tumor specimens, which could potentially aid in the assessment of tumor margin status during BCS.

We develop a method for interpolating skeletal representations (s-reps).We optimize correspondence in an s-rep population via an entropy minimization.Interpolation is used to shift s-rep spokes to improve correspondence.We show improvement in s-reps under several correspondence measures.S-rep-implied PDMs have better correspondence than those from other methods. Statistical analysis of shape representations relies on having good correspondence across a population. Improving correspondence yields improved statistics. Point distribution models (PDMs) are often used to represent object boundaries. Skeletal representations (s-reps) model object widths and boundary directions as well as boundary positions, so they should yield better correspondence.We present two methods: one for continuously interpolating a discretely-sampled skeletal model and one for improving correspondence by using this interpolation to shift skeletal samples to new positions. The interpolation operates by an extension of the mathematics of medial structures. As with Cates' boundary-based method, we evaluate correspondence in terms of regularity and shape-feature population entropies.Evaluation on both synthetic and real data shows that our method both improves correspondence of s-rep models fit to segmented lateral ventricles and that the combined boundary-and-skeletal PDMs implied by these optimized s-reps have better correspondence than optimized boundary PDMs.

This document describes a new class, itk::MorphologicalContourInterpolator, which implements a method proposed by Albu et al. in 2008. Interpolation is done by first determining correspondence between shapes on adjacent segmented slices by detecting overlaps, then aligning the corresponding shapes, generating transition sequence of one-pixel dilations and taking the median as result. Recursion is employed if the original segmented slices are separated by more than one empty slice.This class is n-dimensional, and supports inputs of 3 or more dimensions. `Slices’ are n-1-dimensional, and can be both automatically detected and manually set. The class is efficient in both memory used and execution time. It requires little memory in addition to allocation of input and output images. The implementation is multi-threaded, and processing one of the test inputs takes around 1-2 seconds on a quad-core processor.The class is tested to operate on both itk::Image and itk::RLEImage. Since all the processing is done on extracted slices, usage of itk::RLEImage for input and/or output affects performance to a limited degree.This class is implemented to ease manual segmentation in ITK-SNAP (www.itksnap.org). The class, along with test data and automated regression tests is packaged as an ITK remote module https://github.com/KitwareMedical/ITKMorphologicalContourInterpolation.

We present a scheme that propagates a reference skeletal model (s-rep) into a particular case of an object, thereby propagating the initial shape-related layout of the skeleton-to-boundary vectors, called spokes. The scheme represents the surfaces of the template as well as the target objects by spherical harmonics and computes a warp between these via a thin plate spline. To form the propagated s-rep, it applies the warp to the spokes of the template s-rep and then statistically refines. This automatic approach promises to make s-rep fitting robust for complicated objects, which allows s-rep based statistics to be available to all. The improvement in fitting and statistics is significant compared with the previous methods and in statistics compared with a state-of-the-art boundary based method.

This paper presents a method for automatic color and intensity normalization of digitized histology slides stained with two different agents. In comparison to previous approaches, prior information on the stain vectors is used in the plane estimation process, resulting in improved stability of the estimates. Due to the prevalence of hematoxylin and eosin staining for histology slides, the proposed method has significant practical utility. In particular, it can be used as a first step to standardize appearance across slides and is effective at countering effects due to differing stain amounts and protocols and counteracting slide fading. The approach is validated against non-prior plane-fitting using synthetic experiments and 13 real datasets. Results of application of the method to adjustment of faded slides are given, and the effectiveness of the method in aiding statistical classification is shown.

Purpose: Improving the shape statistics of medical image objects by generating correspondence of interior skeletal points. Data: Synthetic objects and real world lateral ventricles segmented from MR images. Method(s): Each object’s interior is modeled by a skeletal representation called the s-rep, which is a quadrilaterally sampled, folded 2-sided skeletal sheet with spoke vectors proceeding from the sheet to the boundary. The skeleton is divided into three parts: up-side, down-side and fold-curve. The spokes on each part are treated separately and, using spoke interpolation, are shifted along their skeletal parts in each training sample so as to tighten the probability distribution on those spokes’ geometric properties while sampling the object interior regularly. As with the surface-based correspondence method of Cates et al., entropy is used to measure both the probability distribution tightness and sampling regularity. The spokes’ geometric properties are skeletal position, spoke length and spoke direction. The properties used to measure the regularity are the volumetric subregions bounded by the spokes, their quadrilateral sub-area and edge lengths on the skeletal surface and on the boundary. Results: Evaluation on synthetic and real world lateral ventricles demonstrated improvement in the performance of statistics using the resulting probability distributions, as compared to methods based on boundary models. The evaluation measures used were generalization, specificity, and compactness. Conclusions: S-rep models with the proposed improved correspondence provide significantly enhanced statistics as compared to standard boundary models.

We seek a form of object model that exactly and completely captures the interior of most non-branching anatomic objects and simultaneously is well suited for probabilistic analysis on populations of such objects. We show that certain nearly medial, skeletal models satisfy these requirements. These models are first mathematically defined in continuous three-space, and then discrete representations formed by a tuple of spoke vectors are derived. We describe means of fitting these skeletal models into manual or automatic segmentations of objects in a way stable enough to support statistical analysis, and we sketch means of modifying these fits to provide good correspondences of spoke vectors across a training population of objects. Understanding will be developed that these discrete skeletal models live in an abstract space made of a Cartesian product of a Euclidean space and a collection of spherical spaces. Based on this understanding and the way objects change under various rigid and nonrigid transformations, a method analogous to principal component analysis called composite principal nested spheres will be seen to apply to learning a more efficient collection of modes of object variation about a new and more representative mean object than those provided by other representations and other statistical analysis methods. The methods are illustrated by application to hippocampi.

Gray-level quantization (reduction) is an important operation in image processing and analysis. The Lloyd- Max algorithm (LMA) is a classic scalar quantization algorithm that can be used for gray-level reduction with minimal mean squared distortion. However, the algorithm is known to be very sensitive to the choice of initial centers. In this paper, we introduce an adaptive and deterministic algorithm to initialize the LMA for gray-level quantization. Experiments on a diverse set of publicly available test images demonstrate that the presented method outperforms the commonly used uniform initialization method.