Deformable Models

The detection of double edges in x-ray images of lumbar vertebrae is of prime importance in the assessment of vertebral injury or collapse that may be caused by osteoporosis and other spine pathology. In addition, if the above double-edge detection process is conducted within an automatic framework, it would not only facilitate inexpensive and fast means of obtaining objective morphometric measurements on the spine, but also remove the human subjectivity involved in the morphometric analysis. This paper proposes a novel force-formulation scheme, termed as Pressurized Open Directional Gradient Vector Flow snakes, to discriminate and detect the superior and inferior double edges present in the radiographic images of the lumbar vertebrae. As part of the validation process, this algorithm is applied to a set of 100 lumbar images and the detection results are quantified using analyst-generated ground truth. The promising nature of the detection results bears testimony to the efficacy of the proposed approach

"Topological Active Nets are promising parametric deformable models that integrate features of region-based and
boundary-based segmentation techniques. Problems associated with the complexity of the model, however,
have limited their utility. This paper introduces an extension of the model, defining a new behavior for changing
its topology, as well as a novel external force definition and a new local search optimization procedure. In
particular, we propose a new automatic pre-processing phase, a new external energy term based on the Extended
Vector Field Convolution, node movement constraints to avoid crossing links, and different procedures to
perform link cuts and hole detection. Moreover, the new local search procedure also incorporates heuristics to
correct the position of eventually misplaced nodes. The proposal has been tested on 18 synthetic images which
present different segmentation difficulties along with 3 real medical images. Its performance has been compared
with that of the original Topological Active Net optimization approach along with both state-of-the-art
parametric and geometric active contours: two snakes (based on Gradient Vector Flow and Vector Field
Convolution), and two level sets (Chan and Vese, and Geodesic Active Contour). Our new method outperforms
all the others for the given image sets, in terms of segmentation accuracy measured by using four standard
segmentation metrics."

A model for one-dimensional bistable systems characterized by a deformable double-well energy landscape is introduced in order to investigate the effect of shape deformability on the order of phase transition in quantum tunneling and on the quasi-exact integrability of the classical statistical mechanics of these systems. The deformable double-well energy landscape is modeled by a parameterized double-well potential possessing two fixed degenerate minima and a constant barrier height, but a tunable shape of its walls which affects the confinement of the two wells. It is found that unlike bistable models involving

Abstract: In this work, thirteen image-pairs, composed of a color fundus photograph and a scanning laser ophthalmoscope fluorescein angiography (SLO. FA), were registered by rigid, non-rigid and deformable image registration procedures to assess the need for deformable image registration methods when using SLO. FA modalities. Each registration was quantitatively assessed by three different metrics that showed improved performance of the deformable approach. Moreover, the computed deformation grids demonstrated the ...

The topological active nets (TANs) model is a deformable model used for image segmentation. It integrates features of region-based and edge-based segmentation techniques so it is able to fit the contours of the objects and model their inner topology. Also, topological changes in its structure allow the detection of concave and convex contours, holes, and several objects in the scene. Since the model deformation is based on the minimization of an energy functional, the adjustment depends on the minimization algorithm. This paper presents two evolutionary approaches to the energy minimization problem in the TAN model. The first proposal is a genetic algorithm with ad hoc operators whereas the second approach is a hybrid model that combines genetic and greedy algorithms. Both evolutionary approaches improve the accuracy of the segmentation even though only the hybrid model allows topological changes in the model structure.

Abstract—The class of geometric deformable models, so-calledlevel sets, has brought tremendous impact to medical imagery. Inthis paper we present yet another application of level sets to medicalimaging. The method we give here will in a way modify the speedterm in the standard level sets equation of motion. To do so webuild a potential based on the distance and the gradient of theimage we study. In turn the potential gives rise to the force field:FF~ (x,y) = P ∀(p,q)∈I ((x,y)− (p,q)) |∇I(p,q)||(x,y)−(p,q)| 2 . The directionand intensity of the force field at each point will determine thedirection of the contour’s evolution. The images we used to testour method were produced by the Univesite de Sherbrooke’s PET´scanners.Keywords—PET, Cardiac, Heart, Mouse, Geodesic, Geometric,Level Sets, Deformable Models, Edge Detection, Segmentation. I. I NTRODUCTION I N the past decades, image segmentation has played animportant role in medical imaging. Segmented images arenow used routinely in a hu...

The occurrence of stochastic resonance in bistable systems undergoing anomalous diffusions, which arise from densitydependent fluctuations, is investigated with an emphasis on the analytical formulation of the problem as well as a possible analytical derivation of key quantifiers of stochastic resonance. The nonlinear Fokker-Planck equation describing the system dynamics, together with the corresponding Ito-Langevin equation, is formulated. In the linear response regime, analytical expressions of the spectral amplification, of the signal-to-noise ratio and of the hysteresis loop area are derived as quantifiers of stochastic resonance. These quantifiers are found to be strongly dependent on the parameters controlling the type of diffusion; in particular, the peak characterizing the signal-to-noise ratio occurs only in close ranges of parameters. Results introduce the relevant information that, taking into consideration the interactions of anomalous diffusive systems with a periodic signal, can provide a better understanding of the physics of stochastic resonance in bistable systems driven by periodic forces.

Autism is a developmental disorder characterized by social deficits, impaired communication, and restricted and repetitive patterns of behavior (American Psychiatry Association 2000). Various neuropathological studies of autism have revealed abnormalities in several brain regions. Increased head size was the first observed characteristic in children with autism. According to the published studies, different anatomical structures of the brain have been identified as being involved in the abnormal neuro-development associated with autism. Classical neuropathological studies as well as MRI structural findings are consistent with respect to some brain structures, while observations with respect to other structures have differed among studies. This lack of consistency may be due to the sample size as well as to the failure to account for significant confounding factors (e.g., age, sex, IQ, handedness, etc). However, there is an increasing agreement from structural imaging studies on the abnormal anatomy of the white matter (WM) in autistic brains. In addition, the deficits in the size of the corpus callosum

This work presents a method to analyse 3D flat objects and to measure variations of its surface. The method represents of the objects using processsing techniques based on point cloud. The proposed method is focused on the deformation detection of elastic objects which are formed by flat faces. These deformations are usually caused when two bodies, a solid and another elastic object, come in contact and there are contact pressures among their faces. Our method describes an algorithm to estimate the deformation shape. It is done by calculating its skeleton. Particularly, the algorithm calculates the curvature values of the surface points on the object using an analysis of eigenvectors and eigenvalues. Afterwards, the points of the similar curvature are grouped in level curvatures. Finally, a set of the minimum path among level curvatures are calculated to obtain the skeleton. The paper shows a set of experiments which simulate the deformations caused by a robot hand in manipulation tasks of flat objects.

Many image segmentation techniques are available in the literature. Among the available techniques, parametric deformable models play an important role in many medical imaging applications. These models have been proved to be effective in segmenting an anatomic structure using constraints derived from the image data along with a prior knowledge about the location, size and shape of these structures. These models also support highly intuitive interaction mechanisms, which helps medical practitioners to bring their expertise to bear on the model-based image interpretation task. In this paper, a review of nineteen different external forces for the parametric deformable model applied to the medical image segmentation is presented. The main purpose of survey is to identify and discuss each category with its principle, mathematical model, advantages, disadvantages and applications to medical image analysis.

Faced with a vast, dynamic environment, animals and robots often need to acquire and segregate information about ob- jects. The form of their internal representation depends on how the information is utilised. Sometimes it should be compressed and ab- stracted from the original, often complex, sensory information, so it can be efficiently stored and manipulated, for deriving interpreta- tions, causal relationships, functions or affordances. We discuss how salient features of objects can be used to generate compact represen- tations, later allowing for relatively accurate reconstructions and rea- soning. Particular moments in the course of an object-related process can be selected and stored as ‘key frames’. Specifically, we consider the problem of representing and reasoning about a deformable object from the viewpoint of both an artificial and a natural agent.

The topological active nets (TANs) model is a deformable model used for image segmentation. It integrates features of region-based and edge-based segmentation techniques so it is able to fit the contours of the objects and model their inner topology. Also, topological changes in its structure allow the detection of concave and convex contours, holes, and several objects in the scene. Since the model deformation is based on the minimization of an energy functional, the adjustment depends on the minimization algorithm. This paper presents two evolutionary approaches to the energy minimization problem in the TAN model. The first proposal is a genetic algorithm with ad hoc operators whereas the second approach is a hybrid model that combines genetic and greedy algorithms. Both evolutionary approaches improve the accuracy of the segmentation even though only the hybrid model allows topological changes in the model structure.

The linear sampling method is a qualitative procedure for the visualization of both impenetrable and inhomogeneous scatterers, which requires the regularized solution of a linear illposed integral equation of the first kind. An open issue in this technique is the one of determining the optimal scatterer profile from the visualization maps in an automatic manner. In the present paper this problem is addressed in two steps. First, linear sampling is optimized by using a new regularization algorithm for the solution of the integral equation, which provides more accurate maps for different levels of the noise affecting the data. Then an edge detection technique based on active contours is applied to the optimized maps. Our computation exploits a recently introduced implementation of the linear sampling method which enhances both the accuracy and the numerical effectiveness of the approach.

Abstract: In this work, thirteen image-pairs, composed of a color fundus photograph and a scanning laser ophthalmoscope fluorescein angiography (SLO. FA), were registered by rigid, non-rigid and deformable image registration procedures to assess the need for deformable image registration methods when using SLO. FA modalities. Each registration was quantitatively assessed by three different metrics that showed improved performance of the deformable approach. Moreover, the computed deformation grids demonstrated the ...

Mathematical morphology is a novel geometry-based technique for image processing and analysis, originally developed to process binary images, based on the use of simple concepts from set theory and geometry such as set inclusion, intersection, union, complementation, and translation Geometry is used to represent object shape, physics inflict constraints on how the shape may vary over space and time, and optimal approximation theory make available the formal underpinnings of mechanisms for fitting the models to measured data. Deformable curve, surface, and solid models gained popularity after they were proposed by Terzopoulos for use in computer vision and computer graphics in the mid 1980’s introducing the theory of continuous (multidimensional) deformable models in a Lagrangian dynamics setting, based on deformation energies in the form of generalized splines. The deformable model that has attracted the most attention to date is popularly known as “snakes”, planar deformable contours that are useful in several image analysis tasks. They are often used to approximate the locations and shapes of object boundaries in images based on the reasonable assumption that boundaries are piecewise continuous or smooth.
This work presents a novel approach since it joins (and, indeed, reinforces) the index framework with the evaluation of the same biological samples by a suitable combination of deformable models. Nucleus contour is identified through Active Shape Models techniques, and cytoplasm contour’s detected through parametric Snakes, with prior image preprocessing based on statistical and mathematical morphology techniques. Morphometric parameters such as nucleus and cytoplasm area and ratio between them are then easily computed. Biometry was performed using an ocular micrometer and nucleus/cytoplasm ratios were obtained characterizing each of the three identified stages: Immature, Vitellogenic and Mature. This resulted in a collection of tools, called morphological operators, which are eminently suited for the analysis of shape and structure in binary images. Acartia tonsa was used as model to establish an index for oocyte maturity determination based in citometry and histochemical evaluation of gonadic masses. It was validated the application of a methodology with a realistic background and a new, more accurate and ecologically realistic index for oocyte staging emerged.