Unsupervised contour representation and estimation using B-splines and a minimum description length criterion

Plant Species Identification from Occluded Leaf Images

We present an approach to identify the plant species from the contour information from occluded leaf image using a database of full plant leaves. Although contour based 2D shape matching has been studied extensively in the last couple of decades, matching occluded leaves with full leaf databases is an open and little worked on problem. Classifying occluded plant leaves is even more challenging than full leaf matching because of large variations and complexity of leaf structures. Matching an occluded contour with all the full contours in a database is an NP-hard problem, so our algorithm is necessarily suboptimal. First, we represent the 2D contour points as a β-Spline curve. Then, we extract interest points on these curves via the Discrete Contour Evolution (DCE) algorithm. We use subgraph matching using the DCE points as graph nodes, which produces a number of open curves for each closed leaf contour. Next, we compute the similarity transformation parameters (translation, rotation, and uniform scaling) for each open curve. We then "overlay" each open curve with the inverse similarity transformed occluded curve and use the Fréchet distance metric to measure the quality of the match, retaining the best η matched curves. Since the Fréchet metric is cheap to compute but not perfectly correlated with the quality of the match, we formulate an energy functional that is well correlated with the quality of the match, but is considerably more expensive to compute. The functional uses local and global curvature, Shape Context descriptors, and String Cut features. We minimize this energy functional using a convex-concave relaxation framework. The curve among these best η curves, that has the minimum energy, is considered to be the best overall match with the occluded leaf. Experiments on three publicly available leaf image database shows that our method is both effective and efficient, outperforming other current state-of-the-art methods. Occlusion is measured as the percentage of the overall contour (and not leaf area) that is missing. We show that our algorithm can, even for leaves with a high amounts of occlusion (say 50 percent occlusion), still identify the best full leaf match from the databases.

Spline curve deformation model with prior shapes for identifying adhesion boundaries between large lung tumors and tissues around lungs in CT images

PURPOSE

Automated segmentation of lung tumors attached to anatomic structures such as the chest wall or mediastinum remains a technical challenge because of the similar Hounsfield units of these structures. To address this challenge, we propose herein a spline curve deformation model that combines prior shapes to correct large spatially contiguous errors (LSCEs) in input shapes derived from image-appearance cues.The model is then used to identify the adhesion boundaries between large lung tumors and tissue around the lungs.

METHODS

The deformation of the whole curve is driven by the transformation of the control points (CPs) of the spline curve, which are influenced by external and internal forces. The external force drives the model to fit the positions of the non-LSCEs of the input shapes while the internal force ensures the local similarity of the displacements of the neighboring CPs. The proposed model corrects the gross errors in the lung input shape caused by large lung tumors, where the initial lung shape for the model is inferred from the training shapes by shape group-based sparse prior information and the input lung shape is inferred by adaptive-thresholding-based segmentation followed by morphological refinement.

RESULTS

The accuracy of the proposed model is verified by applying it to images of lungs with either moderate large-sized (ML) tumors or giant large-sized (GL) tumors. The quantitative results in terms of the averages of the dice similarity coefficient (DSC) and the Jaccard similarity index (SI) are 0.982 ± 0.006 and 0.965 ± 0.012 for segmentation of lungs adhered by ML tumors, and 0.952 ± 0.048 and 0.926 ± 0.059 for segmentation of lungs adhered by GL tumors, which give 0.943 ± 0.021 and 0.897 ± 0.041 for segmentation of the ML tumors, and 0.907 ± 0.057 and 0.888 ± 0.091 for segmentation of the GL tumors, respectively. In addition, the bidirectional Hausdorff distances are 5.7 ± 1.4 and 11.3 ± 2.5 mm for segmentation of lungs with ML and GL tumors, respectively.

CONCLUSIONS

When combined with prior shapes, the proposed spline curve deformation can deal with large spatially consecutive errors in object shapes obtained from image-appearance information. We verified this method by applying it to the segmentation of lungs with large tumors adhered to the tissue around the lungs and the large tumors. Both the qualitative and quantitative results are more accurate and repeatable than results obtained with current state-of-the-art techniques.

Automatic Muscle Fiber Orientation Tracking in Ultrasound Images Using a New Adaptive Fading Bayesian Kalman Smoother

This paper proposes a new algorithm for automatic estimation of muscle fiber orientation (MFO) in musculoskeletal ultrasound images, which is commonly used for both diagnosis and rehabilitation assessment of patients. The algorithm is based on a novel adaptive fading Bayesian Kalman filter (AF-BKF) and an automatic region of interest (ROI) extraction method. The ROI is first enhanced by the Gabor filter (GF) and extracted automatically using the revoting constrained Radon transform (RCRT) approach. The dominant MFO in the ROI is then detected by the RT and tracked by the proposed AF-BKF, which employs simplified Gaussian mixtures to approximate the non-Gaussian state densities and a new adaptive fading method to update the mixture parameters. An AF-BK smoother (AF-BKS) is also proposed by extending the AF-BKF using the concept of Rauch-Tung-Striebel smoother for further smoothing the fascicle orientations. The experimental results and comparisons show that: 1) the maximum segmentation error of the proposed RCRT is below nine pixels, which is sufficiently small for MFO tracking; 2) the accuracy of MFO gauged by RT in the ROI enhanced by the GF is comparable to that of using multiscale vessel enhancement filter-based method and better than those of local RT and revoting Hough transform approaches; and 3) the proposed AF-BKS algorithm outperforms the other tested approaches and achieves a performance close to those obtained by experienced operators (the overall covariance obtained by the AF-BKS is 3.19, which is rather close to that of the operators, 2.86). It, thus, serves as a valuable tool for automatic estimation of fascicle orientations and possibly for other applications in musculoskeletal ultrasound images.

Contour-Seed Pairs Learning-Based Framework for Simultaneously Detecting and Segmenting Various Overlapping Cells/Nuclei in Microscopy Images

In this paper, we propose a novel contour-seed pairs learning-based framework for robust and automated cell/nucleus segmentation. Automated granular object segmentation in microscopy images has significant clinical importance for pathology grading of the cell carcinoma and gene expression. The focus of the past literature is dominated by either segmenting a certain type of cells/nuclei or simply splitting the clustered objects without contours inference of them. Our method addresses these issues by formulating the detection and segmentation tasks in terms of a unified regression problem, where a cascade sparse regression chain model is trained and then applied to return object locations and entire boundaries of clustered objects. In particular, we first learn a set of online convolutional features in each layer. Then, in the proposed cascade sparse regression chain, with the input from the learned features, we iteratively update the locations and clustered object boundaries until convergence. In this way, the boundary evidences of each individual object can be easily delineated and be further fed to a complete contour inference procedure optimized by the minimum description length principle. For any probe image, our method enables to analyze free-lying and overlapping cells with complex shapes. Experimental results show that the proposed method is very generic and performs well on contour inferences of various cell/nucleus types. Compared with the current segmentation techniques, our approach achieves state-of-the-art performances on four challenging datasets, i.e., the kidney renal cell carcinoma histopathology dataset, Drosophila Kc167 cellular dataset, differential interference contrast red blood cell dataset, and cervical cytology dataset.

Landmark-Based Shape Encoding and Sparse-Dictionary Learning in the Continuous Domain

We provide a generic framework to learn shape dictionaries of landmark-based curves that are defined in the continuous domain. We first present an unbiased alignment method that involves the construction of a mean shape as well as training sets whose elements are subspaces that contain all affine transformations of the training samples. The alignment relies on orthogonal projection operators that have a closed form. We then present algorithms to learn shape dictionaries according to the structure of the data that needs to be encoded: 1) projection-based functional principal-component analysis for homogeneous data and 2) continuous-domain sparse shape encoding to learn dictionaries that contain imbalanced data, outliers, or different types of shape structures. Through parametric spline curves, we provide a detailed and exact implementation of our method. We demonstrate that it requires fewer parameters than purely discrete methods and that it is computationally more efficient and accurate. We illustrate the use of our framework for dictionary learning of structures in biomedical images as well as for shape analysis in bioimaging.

Multiresolution Subdivision Snakes

We present a new family of snakes that satisfy the property of multiresolution by exploiting subdivision schemes. We show in a generic way how to construct such snakes based on an admissible subdivision mask. We derive the necessary energy formulations and provide the formulas for their efficient computation. Depending on the choice of the mask, such models have the ability to reproduce trigonometric or polynomial curves. They can also be designed to be interpolating, a property that is useful in user-interactive applications. We provide explicit examples of subdivision snakes and illustrate their use for the segmentation of bioimages. We show that they are robust in the presence of noise and provide a multiresolution algorithm to enlarge their basin of attraction, which decreases their dependence on initialization compared to singleresolution snakes. We show the advantages of the proposed model in terms of computation and segmentation of structures with different sizes.

Local Transverse-Slice-Based Level-Set Method for Segmentation of 3-D High-Frequency Ultrasonic Backscatter From Dissected Human Lymph Nodes

OBJECTIVE

To detect metastases in freshly excised human lymph nodes (LNs) using three-dimensional (3-D), high-frequency, quantitative ultrasound (QUS) methods, the LN parenchyma (LNP) must be segmented to preclude QUS analysis of data in regions outside the LNP and to compensate ultrasound attenuation effects due to overlying layers of LNP and residual perinodal fat (PNF).

METHODS

After restoring the saturated radio-frequency signals from PNF using an approach based on smoothing cubic splines, the three regions, i.e., LNP, PNF, and normal saline (NS), in the LN envelope data are segmented using a new, automatic, 3-D, three-phase, statistical transverseslice-based level-set (STS-LS) method that amends Lankton's method. Due to ultrasound attenuation and focusing effects, the speckle statistics of the envelope data vary with imaged depth. Thus, to mitigate depth-related inhomogeneity effects, the STS-LS method employs gamma probabilitydensity functions to locally model the speckle statistics within consecutive transverse slices.

RESULTS

Accurate results were obtained on simulated data. On a representative dataset of 54 LNs acquired from colorectal-cancer patients, the Dice similarity coefficient for LNP, PNF, and NS were 0.938 ± 0.025, 0.832 ± 0.086, and 0.968 ± 0.008, respectively, when compared to expert manual segmentation.

CONCLUSION

The STS-LS outperforms the established methods based on global and local statistics in our datasets and is capable of accurately handling the depth-dependent effects due to attenuation and focusing.

SIGNIFICANCE

This advance permits the automatic QUS-based cancer detection in the LNs. Furthermore, the STS-LS method could potentially be used in a wide range of ultrasound-imaging applications suffering from depth-dependent effects.

Hermite Snakes With Control of Tangents

We introduce a new model of parametric contours defined in a continuous fashion. Our curve model relies on Hermite spline interpolation and can easily generate curves with sharp discontinuities; it also grants direct access to the tangent at each location. With these two features, the Hermite snake distinguishes itself from classical spline-snake models and allows one to address certain bioimaging problems in a more efficient way. More precisely, the Hermite snake construction allows introducing sharp corners in the snake curve and designing directional energy functionals relying on local orientation information in the input image. Using the formalism of spline theory, the model is shown to meet practical requirements such as invariance to affine transformations and good approximation properties. Finally, the dependence on initial conditions and the robustness to the noise is studied on synthetic data in order to validate our Hermite snake model, and its usefulness is illustrated on real biological images acquired using brightfield, phase-contrast, differential-interference-contrast, and scanning-electron microscopy.

Shapes From Pixels

Continuous-domain visual signals are usually captured as discrete (digital) images. This operation is not invertible in general, in the sense that the continuous-domain signal cannot be exactly reconstructed based on the discrete image, unless it satisfies certain constraints (e.g., bandlimitedness). In this paper, we study the problem of recovering shape images with smooth boundaries from a set of samples. Thus, the reconstructed image is constrained to regenerate the same samples (consistency), as well as forming a shape (bilevel) image. We initially formulate the reconstruction technique by minimizing the shape perimeter over the set of consistent binary shapes. Next, we relax the non-convex shape constraint to transform the problem into minimizing the total variation over consistent non-negative-valued images. We also introduce a requirement (called reducibility) that guarantees equivalence between the two problems. We illustrate that the reducibility property effectively sets a requirement on the minimum sampling density. We also evaluate the performance of the relaxed alternative in various numerical experiments.

Spline-based deforming ellipsoids for interactive 3D bioimage segmentation

We present a new fast active-contour model (a.k.a. snake) for image segmentation in 3D microscopy. We introduce a parametric design that relies on exponential B-spline bases and allows us to build snakes that are able to reproduce ellipsoids. We design our bases to have the shortest-possible support, subject to some constraints. Thus, computational efficiency is maximized. The proposed 3D snake can approximate blob-like objects with good accuracy and can perfectly reproduce spheres and ellipsoids, irrespective of their position and orientation. The optimization process is remarkably fast due to the use of Gauss' theorem within our energy computation scheme. Our technique yields successful segmentation results, even for challenging data where object contours are not well defined. This is due to our parametric approach that allows one to favor prior shapes. In addition, this paper provides a software that gives full control over the snakes via an intuitive manipulation of few control points.

Image analysis and length estimation of biomolecules using AFM

There are many examples of problems in pattern analysis for which it is often possible to obtain systematic characterizations, if in addition a small number of useful features or parameters of the image are known a priori or can be estimated reasonably well. Often the relevant features of a particular pattern analysis problem are easy to enumerate, as when statistical structures of the patterns are well understood from the knowledge of the domain. We study a problem from molecular image analysis, where such a domain-dependent understanding may be lacking to some degree and the features must be inferred via machine-learning techniques. In this paper, we propose a rigorous, fully-automated technique for this problem. We are motivated by an application of atomic force microscopy (AFM) image processing needed to solve a central problem in molecular biology, aimed at obtaining the complete transcription profile of a single cell, a snapshot that shows which genes are being expressed and to what degree. Reed et al (Single molecule transcription profiling with AFM, Nanotechnology, 18:4, 2007) showed the transcription profiling problem reduces to making high-precision measurements of biomolecule backbone lengths, correct to within 20-25 bp (6-7.5 nm). Here we present an image processing and length estimation pipeline using AFM that comes close to achieving these measurement tolerances. In particular, we develop a biased length estimator on trained coefficients of a simple linear regression model, biweighted by a Beaton-Tukey function, whose feature universe is constrained by James-Stein shrinkage to avoid overfitting. In terms of extensibility and addressing the model selection problem, this formulation subsumes the models we studied.

Snakes with an ellipse-reproducing property

We present a new class of continuously defined parametric snakes using a special kind of exponential splines as basis functions. We have enforced our bases to have the shortest possible support subject to some design constraints to maximize efficiency. While the resulting snakes are versatile enough to provide a good approximation of any closed curve in the plane, their most important feature is the fact that they admit ellipses within their span. Thus, they can perfectly generate circular and elliptical shapes. These features are appropriate to delineate cross sections of cylindrical-like conduits and to outline bloblike objects. We address the implementation details and illustrate the capabilities of our snake with synthetic and real data.

Registering preprocedure volumetric images with intraprocedure 3-D ultrasound using an ultrasound imaging model

For many image-guided interventions there exists a need to compute the registration between preprocedure image(s) and the physical space of the intervention. Real-time intraprocedure imaging such as ultrasound (US) can be used to image the region of interest directly and provide valuable anatomical information for computing this registration. Unfortunately, real-time US images often have poor signal-to-noise ratio and suffer from imaging artefacts. Therefore, registration using US images can be challenging and significant preprocessing is often required to make the registrations robust. In this paper we present a novel technique for computing the image-to-physical registration for minimally invasive cardiac interventions using 3-D US. Our technique uses knowledge of the physics of the US imaging process to reduce the amount of preprocessing required on the 3-D US images. To account for the fact that clinical US images normally undergo significant image processing before being exported from the US machine our optimization scheme allows the parameters of the US imaging model to vary. We validated our technique by computing rigid registrations for 12 cardiac US/magnetic resonance imaging (MRI) datasets acquired from six volunteers and two patients. The technique had mean registration errors of 2.1-4.4 mm, and 75% capture ranges of 5-30 mm. We also demonstrate how the same approach can be used for respiratory motion correction: on 15 datasets acquired from five volunteers the registration errors due to respiratory motion were reduced by 45%-92%.

Region segmentation in the frequency domain applied to upper airway real-time magnetic resonance images

We describe a method for unsupervised region segmentation of an image using its spatial frequency domain representation. The algorithm was designed to process large sequences of real-time magnetic resonance (MR) images containing the 2-D midsagittal view of a human vocal tract airway. The segmentation algorithm uses an anatomically informed object model, whose fit to the observed image data is hierarchically optimized using a gradient descent procedure. The goal of the algorithm is to automatically extract the time-varying vocal tract outline and the position of the articulators to facilitate the study of the shaping of the vocal tract during speech production.

Automatic microarray spot segmentation using a Snake-Fisher model

Inspired by Paragious and Deriche's work, which unifies boundary-based and region-based image partition approaches, we integrate the snake model and the Fisher criterion to capture, respectively, the boundary information and region information of microarray images. We then use the proposed algorithm to segment the spots in the microarray images, and compare our results with those obtained by commercial software. Our algorithm is automatic because the parameters are adaptively estimated from the data without human intervention.

Robust shape tracking with multiple models in ultrasound images

This paper addresses object tracking in ultrasound images using a robust multiple model tracker. The proposed tracker has the following features: 1) it uses multiple dynamic models to track the evolution of the object boundary, and 2) it models invalid observations (outliers), reducing their influence on the shape estimates. The problem considered in this paper is the tracking of the left ventricle which is known to be a challenging problem. The heart motion presents two phases (diastole and systole) with different dynamics, the multiple models used in this tracker try to solve this difficulty. In addition, ultrasound images are corrupted by strong multiplicative noise which prevents the use of standard deformable models. Robust estimation techniques are used to address this difficulty. The multiple model data association (MMDA) tracker proposed in this paper is based on a bank of nonlinear filters, organized in a tree structure. The algorithm determines which model is active at each instant of time and updates its state by propagating the probability distribution, using robust estimation techniques.

Repulsive force based snake model to segment and track neuronal axons in 3D microscopy image stacks

The branching patterns of axons and dendrites are fundamental structural properties that affect the synaptic connectivity of axons. Although today three-dimensional images of fluorescently labeled processes can be obtained to study axonal branching, there are no robust methods of tracing individual axons. This paper describes a repulsive force based snake model to segment and track axonal profiles in 3D images. This new method segments all the axonal profiles in a 2D image and then uses the results obtained from that image as prior information to help segment the adjacent 2D image. In this way, the segmentation successfully connects axonal profiles over hundreds of images in a 3D image stack. Individual axons can then be extracted based on the segmentation results. The utility and performance of the method are demonstrated using 3D axonal images obtained from transgenic mice that express fluorescent protein.

Minimal stochastic complexity image partitioning with unknown noise model

We present a generalization of a new statistical technique of image partitioning into homogeneous regions to cases where the family of the probability laws of the gray-level fluctuations is a priori unknown. For that purpose, the probability laws are described with step functions whose parameters are estimated. This approach is based on a polygonal grid which can have an arbitrary topology and whose number of regions and regularity of its boundaries are obtained by minimizing the stochastic complexity of the image. We demonstrate that efficient homogeneous image partitioning can be obtained when no parametric model of the probability laws of the gray levels is used and that this approach leads to a criterion without parameter to be tuned by the user. The efficiency of this technique is compared to a statistical parametric technique on a synthetic image and is compared to a standard unsupervised segmentation method on real optical images.

Nonparametric statistical snake based on the minimum stochastic complexity

We propose a nonparametric statistical snake technique that is based on the minimization of the stochastic complexity (minimum description length principle). The probability distributions of the gray levels in the different regions of the image are described with step functions with parameters that are estimated. The segmentation is thus obtained by minimizing a criterion that does not include any parameter to be tuned by the user. We illustrate the robustness of this technique on various types of images with level set and polygonal contour models. The efficiency of this approach is also analyzed in comparison with parametric statistical techniques.

Ultrasound image segmentation: a survey

This paper reviews ultrasound segmentation paper methods, in a broad sense, focusing on techniques developed for medical B-mode ultrasound images. First, we present a review of articles by clinical application to highlight the approaches that have been investigated and degree of validation that has been done in different clinical domains. Then, we present a classification of methodology in terms of use of prior information. We conclude by selecting ten papers which have presented original ideas that have demonstrated particular clinical usefulness or potential specific to the ultrasound segmentation problem.

Biventricular myocardial strains via nonrigid registration of anatomical NURBS model [corrected]

We present research in which both left and right ventricular deformation is estimated from tagged cardiac magnetic resonance imaging using volumetric deformable models constructed from nonuniform rational B-splines (NURBS). The four model types considered and compared for the left ventricle include two Cartesian NURBS models--one with a cylindrical parameter assignment and one with a prolate spheroidal parameter assignment. The remaining two are non-Cartesian, i.e., prolate spheroidal and cylindrical each with their respective prolate spheroidal and cylindrical parameter assignment regimes. These choices were made based on the typical shape of the left ventricle. For each frame starting with end-diastole, a NURBS model is constructed by fitting two surfaces with the same parameterization to the corresponding set of epicardial and endocardial contours from which a volumetric model is created. Using normal displacements of the three sets of orthogonal tag planes as well as displacements of contour/tag line intersection points and tag plane intersection points, one can solve for the optimal homogeneous coordinates, in a weighted least squares sense, of the control points of the deformed NURBS model at end-diastole using quadratic programming. This allows for subsequent nonrigid registration of the biventricular model at end-diastole to all later time frames. After registration of the model to all later time points, the registered NURBS models are temporally lofted in order to create a comprehensive four-dimensional NURBS model. From the lofted model, we can extract three-dimensional myocardial deformation fields and corresponding Lagrangian and Eulerian strain maps which are local measures of nonrigid deformation. The results show that, in the case of simulated data, the quadratic Cartesian NURBS models with the cylindrical and prolate spheroidal parameter assignments outperform their counterparts in predicting normal strain. The decreased complexity associated with the Cartesian model with the cylindrical parameter assignment prompted its use for subsequent calculations. Lagrangian strains in three canine data, a normal human, and a patient with history of myocardial infarction are presented. Eulerian strains for the normal human data are also included.

Dorsoventral Extension of the Talairach Transformation and Its Automatic Calculation for Magnetic Resonance Neuroimages

The Talairach transformation (TT), the most prevalent method for brain normalization and atlas-to-data warping, is conceptually simple, fast and can be automated. Two problems with the TT in the clinical setting that are addressed in this article are reduced accuracy at the orbitofrontal cortex and upper corpus callosum (CC) and unsuitability for functional neurosurgery because of incomplete scanning. To increase dorsoventral accuracy, we introduce 2 additional landmarks: the top of the CC (SM) and the most ventral point of the orbitofrontal cortex on the midsagittal slab (IM). A method for their automatic calculation is proposed and validated against 55 diversified magnetic resonance (MR) imaging cases. The SM and IM landmarks are identified accurately and robustly in an automatic way. The average error of SM localization is 0.69 mm, and 91% of all cases have an error not greater than 1 mm. The average error of IM localization is 0.98 mm, approximately three quarters of cases have an error not greater than 1 mm, and 95% of all cases have an error not larger than 2 mm. The SM is correlated (R(2) = 0.72) with the most superior cortical landmark, whereas the IM is only loosely correlated (R(2) = 0.22) with the most inferior cortical landmark. On average, the original TT overlays the atlas axial plate at -24 on the orbitofrontal cortex as opposed to the correct plate at -28. Therefore, 1-dimensional ventral scaling in the original TT is insufficient to cope with variability in the orbitofrontal cortex. The key advantages of our approach are the preserved conceptual simplicity of the TT, fully automatic identification of the new landmarks, improved accuracy of the atlas-to-data match without compromising performance, and enabled TT use in functional neurosurgery when a dorsal part of the brain is not available in the scan.

Minimal stochastic complexity snake-based technique adapted to an unknown noise model

We propose a polygonal snake segmentation technique adapted to objects that can be composed of several regions with gray-level fluctuations described by a priori unknown probability laws. This approach is based on a histogram equalization and on the minimization of a criterion without parameter to be tuned by the user. We demonstrate the efficiency of this approach, which has low computational cost, on synthetic and real images perturbed by different types of optical noise.

Intravital leukocyte detection using the gradient inverse coefficient of variation

The problem of identifying and counting rolling leukocytes within intravital microscopy is of both theoretical and practical interest. Currently, methods exist for tracking rolling leukocytes in vivo, but these methods rely on manual detection of the cells. In this paper we propose a technique for accurately detecting rolling leukocytes based on Bayesian classification. The classification depends on a feature score, the gradient inverse coefficient of variation (GICOV), which serves to discriminate rolling leukocytes from a cluttered environment. The leukocyte detection process consists of three sequential steps: the first step utilizes an ellipse matching algorithm to coarsely identify the leukocytes by finding the ellipses with a locally maximal GICOV. In the second step, starting from each of the ellipses found in the first step, a B-spline snake is evolved to refine the leukocytes boundaries by maximizing the associated GICOV score. The third and final step retains only the extracted contours that have a GICOV score above the analytically determined threshold. Experimental results using 327 rolling leukocytes were compared to those of human experts and currently used methods. The proposed GICOV method achieves 78.6% leukocyte detection accuracy with 13.1% false alarm rate.

Segmentation of fetal ultrasound images

This paper describes a new method for segmentation of fetal anatomic structures from echographic images. More specifically, we estimate and measure the contours of the femur and of cranial cross-sections of fetal bodies, which can thus be automatically measured. Contour estimation is formulated as a statistical estimation problem, where both the contour and the observation model parameters are unknown. The observation model (or likelihood function) relates, in probabilistic terms, the observed image with the underlying contour. This likelihood function is derived from a region-based statistical image model. The contour and the observation model parameters are estimated according to the maximum likelihood (ML) criterion, via deterministic iterative algorithms. Experiments reported in the paper, using synthetic and real images, testify for the adequacy and good performance of the proposed approach.

Entropy of partially polarized light and application to statistical processing techniques

We have analyzed entropy properties of coherent and partially polarized light in an arbitrary number of spatial dimensions. We show that for Gaussian fields, the Shannon entropy is a simple function of the intensity and of the Barakat degree of polarization. In particular, we provide a probabilistic interpretation of this definition of the degree of polarization. Using information theory results, we also deduce some physical properties of partially polarized light such as additivity of the entropy and depolarization effects induced by mixing partially polarized states of light. Finally, we demonstrate that entropy measures can play an important role in segmentation and detection tasks.

Efficient energies and algorithms for parametric snakes

Parametric active contour models are one of the preferred approaches for image segmentation because of their computational efficiency and simplicity. However, they have a few drawbacks which limit their performance. In this paper, we identify some of these problems and propose efficient solutions to get around them. The widely-used gradient magnitude-based energy is parameter dependent; its use will negatively affect the parametrization of the curve and, consequently, its stiffness. Hence, we introduce a new edge-based energy that is independent of the parameterization. It is also more robust since it takes into account the gradient direction as well. We express this energy term as a surface integral, thus unifying it naturally with the region-based schemes. The unified framework enables the user to tune the image energy to the application at hand. We show that parametric snakes can guarantee low curvature curves, but only if they are described in the curvilinear abscissa. Since normal curve evolution do not ensure constant arc-length, we propose a new internal energy term that will force this configuration. The curve evolution can sometimes give rise to closed loops in the contour, which will adversely interfere with the optimization algorithm. We propose a curve evolution scheme that prevents this condition.

Contrast definition for optical coherent polarimetric images

We consider polarimetric images formed with coherent waves, such as in laser-illuminated imagery or synthetic aperture radar. A definition of the contrast between regions with different polarimetric properties in such images is proposed, and it is shown that the performances of maximum likelihood-based detection and segmentation algorithms are bijective functions of this contrast parameter. This makes it possible to characterize the performance of such algorithms by simply specifying the value of the contrast parameter.

Influence of the noise model on level set active contour segmentation

We analyze level set implementation of region snakes based on the maximum likelihood method for different noise models that belong to the exponential family. We show that this approach can improve segmentation results in noisy images and we demonstrate that the regularization term can be efficiently determined using an information theory-based approach, i.e., the minimum description length principle. The criterion to be optimized has no free parameter to be tuned by the user and the obtained segmentation technique is adapted to nonsimply connected objects.

Minimum description length synthetic aperture radar image segmentation

We present a new minimum description length (MDL) approach based on a deformable partition--a polygonal grid--for automatic segmentation of a speckled image composed of several homogeneous regions. The image segmentation thus consists in the estimation of the polygonal grid, or, more precisely, its number of regions, its number of nodes and the location of its nodes. These estimations are performed by minimizing a unique MDL criterion which takes into account the probabilistic properties of speckle fluctuations and a measure of the stochastic complexity of the polygonal grid. This approach then leads to a global MDL criterion without an undetermined parameter since no other regularization term than the stochastic complexity of the polygonal grid is necessary and noise parameters can be estimated with maximum likelihood-like approaches. The performance of this technique is illustrated on synthetic and real synthetic aperture radar images of agricultural regions and the influence of different terms of the model is analyzed.

A MAP framework for tag line detection in SPAMM data using Markov random fields on the B-spline solid

Magnetic resonance (MR) tagging is a technique for measuring heart deformations through creation of a stripe grid pattern on cardiac images. In this paper, we present a maximum a posteriori (MAP) framework for detecting tag lines using a Markov random field (MRF) defined on the lattice generated by three-dimensional (3-D) and four-dimensional (4-D) (3-D + t) uniform sampling of B-spline models. In the 3-D case, MAP estimation is cast for detecting present tag features in the current image given an initial solid from the previous frame (the initial undeformed solid is manually positioned by clicking on corner points of a cube). The method also allows the parameters of the solid model, including the number of knots and the spline order, to be adjusted within the same framework. Fitting can start with a solid with less knots and lower spline order and proceed to one with more knots and/or higher order so as to achieve more accuracy and/or higher order of smoothness. In the 4-D case, the initial model is considered to be the linear interpolation of a sequence of optimal solids obtained from 3-D tracking. The same framework proposed for the 3-D case can once again be applied to arrive at a 4-D B-spline model with a higher temporal order.

Minimal-complexity segmentation with a polygonal snake adapted to different optical noise models

Polygonal active contours (snakes) have been used with success for target segmentation and tracking. We propose to adapt a technique based on the minimum description length principle to estimate the complexity (proportional to the number of nodes) of the polygon used for the segmentation. We demonstrate that, provided that an up-and-down multiresolution strategy is implemented, it is possible to estimate efficiently this number of nodes without a priori knowledge and with a fast algorithm, leading to a segmentation criterion without free parameters. We also show that, for polygonal-shaped objects, this new technique leads to better results than using a simple regularization strategy based on the smoothness of the contour.