Image segmentation plays a crucial role in many medical-imaging applications, by automating or facilitating the delineation of anatomical structures and other regions of interest. We present a critical appraisal of the current status of semi-automated and automated methods for the segmentation of anatomical medical images. Terminology and important issues in image segmentation are first presented. Current segmentation approaches are then reviewed with an emphasis on the advantages and disadvantages of these methods for medical imaging applications. We conclude with a discussion on the future of image segmentation methods in biomedical research.

Summary: Accuracy in in vivo quantitation of brain func tion with positron emission tomography (PET) has often been limited by partial volume effects. This limitation be comes prominent in studies of aging and degenerative brain diseases where partial volume effects vary with dif ferent degrees of atrophy. The present study describes how the actual gray matter (GM) tracer concentration can be estimated using an algorithm that relates the regional fraction of GM to partial volume effects. The regional fraction of GM was determined by magnetic resonance imaging (MRI). The procedure is designated as GM PET. In computer simulations and phantom studies, the GM PET algorithm permitted a 100% recovery of the actual tracer concentration in neocortical GM and hippocam pus, irrespective of the GM volume. GM PET was apPositron emission tomography (PET) permits in vestigation of physiological and biochemical pro cesses in human brain in vivo, and has yielded new insights into both normal physiology and diseases (Kuhl et aI. , 1982;Foster, 1983; Wagner et aI. , 1983; Frost et aI., 1985;Phelps and Mazziotta, 1985;Frost, 1986; Yamaguchi et aI. , 1986; Yoshii et aI., Abbreviations used: AU, arbitrary units; FWHM, full width at half-maximum; OM, gray matter; MRI, magnetic resonance im aging; PET, positron emission tomography; RMSE, relative mean-squared error; ROI, region of interest; SPOR, spoiled grass; WM, white matter. 571plied in a test case of temporal lobe epilepsy revealing an increase in radiotracer activity in GM that was undetec ted in the PET image before correction for partial volume effects. In computer simulations, errors in the segmenta tion of GM and errors in registration of PET and MRI images resulted in less than 15% inaccuracy in the GM PET image. In conclusion, GM PET permits accurate de termination of the actual radiotracer concentration in hu man brain GM in vivo. The method differentiates whether a change in the apparent radiotracer concentration re flects solely an alteration in GM volume or rather a change in radiotracer concentration per unit volume of GM. Key Words: Brain gray matter-Positron emission tomography-Magnetic resonance imaging-Partial vol ume effects-Aging-Dementia-Brain atrophy.1988; Fowler, 1990; Frost and Wagner, 1990; Leen ders et aI., 1990;Martin et al., 1991; Mayberg et aI. , 1991). Nevertheless, a limitation of PET remains: its relatively poor spatial resolution. As a result, PET quantification, especially in structures smaller than two times the full width at half-maximum (FWHM) of the tomograph, is affected by partial volume effects (Hoffmann et aI. , 1979). Given that the in-plane FWHM of current PET instruments ranges from 2.6 mm (Valk et aI. , 1990) to about 14 mm, tracer activity in many brain structures, in cluding the neocortex, is often underestimated. In neocortex, gray matter (GM), white matter (WM), and cerebrospinal fluid (CSF) spaces are convo luted, and cannot be resolved using PET instrumen tation; a cortical PET signal thus reflects the aver age tracer concentr...

Active contours, or snakes, are used extensively in computer vision and image processing applications, particularly to locate object boundaries. A new type of external force for active contours, called gradient vector flow (GVF) was introduced recently to address problems associated with initialization and poor convergence to boundary concavities. GVF is computed as a diffusion of the gradient vectors of a gray-level or binary edge map derived from the image. In this paper, we generalize the GVF formulation to include two spatially varying weighting functions. This improves active contour convergence to long, thin boundary indentations, while maintaining other desirable properties of GVF, such as an extended capture range. The original GVF is a special case of this new generalized GVF (GGVF) model. An error analysis for active contour results on simulated test images is also presented.1998 Elsevier Science B.V. All rights reserved. ZusammenfassungAktive Umrisse, oder Schlangen, werden vielfach in Computervision-und Bildverarbeitungs-Anwendungen benutzt, um insbesondere Objektgrenzen zu lokalisieren. Ein neuer Typ a¨u{erer Kra¨fte fu¨r aktive Umrisse, Gradient »ector Flow (GVF) genannt, wurde ku¨rzlich eingefu¨hrt, um Probleme anzusprechen, die mit Initialisierung und schlechter Konvergenz zu Grenzkonkavita¨ten zusammenha¨ngen. GVF wird als eine Diffusion des Gradientenvektors einer Graustufen-oder 'Binary Edge'-Karte berechnet, die aus dem Bild gewonnen werden. In diesem Artikel verallgemeinern wir die GVF Formulierung, so da{ zwei ra¨umlich variierende Gewichtsfunktionen eingeschlossen werden. Dies verbessert die Konvergenz aktiver Umrisse zu langen, du¨nnen Grenzmarkierungen, wa¨hrend andere wu¨nschenswerte Eigenschaften des GVF, wie erweiterter Einfangbereich, erhalten bleiben. Das urspru¨ngliche GVF ist ein Spezialfall dieses neuen verallgemeinerten GVF (GGVF) Modells. Eins Fehleranalyse von Ergebnissen aktiver Umrisse mit simulierten Testbildern wird ebenfalls pra¨sentiert.1998 Elsevier Science B.V. All rights reserved. contours actifs, appele`flux de vecteurs gradients (FVG) a e´te´introduit re´cemment pour traiter les proble´mes associe´s a`l'initialisation et la faible convergence vers des concavite´s dans les contours. Le FVG est calcule´comme une diffusion des vecteurs gradients d'une carte des contours d'une image en niveaux de gris ou binaire. Dans cet article, nous ge´ne´ralisons la formulation du FVG pour y inclure deux fonctions de poids a`variation spatiale. Ceci ame´liore la convergence des contours actifs vers les indentations de contours fines et longues, tout en maintenant les autres proprie´te´s inte´ressantes des FVG comme la plage de capture e´tendue. Les FVG originaux sont un cas particulier des mode`les de FVG ge´ne´ralise´s. Une analyse de l'erreur des re´sultats de contours actifs sur des images de test synthe´tiques est aussi pre´sente´e.

An algorithm is presented for the fuzzy segmentation of two-dimensional (2-D) and three-dimensional (3-D) multispectral magnetic resonance (MR) images that have been corrupted by intensity inhomogeneities, also known as shading artifacts. The algorithm is an extension of the 2-D adaptive fuzzy C-means algorithm (2-D AFCM) presented in previous work by the authors. This algorithm models the intensity inhomogeneities as a gain field that causes image intensities to smoothly and slowly vary through the image space. It iteratively adapts to the intensity inhomogeneities and is completely automated. In this paper, we fully generalize 2-D AFCM to three-dimensional (3-D) multispectral images. Because of the potential size of 3-D image data, we also describe a new faster multigrid-based algorithm for its implementation. We show, using simulated MR data, that 3-D AFCM yields lower error rates than both the standard fuzzy C-means (FCM) algorithm and two other competing methods, when segmenting corrupted images. Its efficacy is further demonstrated using real 3-D scalar and multispectral MR brain images.