Estimation of vector fields in unconstrained and inequality constrained variational problems for segmentation and registration

Vector fields arise in many problems of computer vision, particularly in non-rigid registration. In this paper, we develop coupled partial differential equations (PDEs) to estimate vector fields that define the deformation between objects, and the contour or surface that defines the segmentation of the objects as well.We also explore the utility of inequality constraints applied to variational problems in vision such as estimation of deformation fields in non-rigid registration and tracking. To solve inequality constrained vector field estimation problems, we apply tools from the Kuhn-Tucker theorem in optimization theory. Our technique differs from recently popular joint segmentation and registration algorithms, particularly in its coupled set of PDEs derived from the same set of energy terms for registration and segmentation. We present both the theory and results that demonstrate our approach

3D ball skinning using PDEs for generation of smooth tubular surfaces

We present an approach to compute a smooth, interpolating skin of an ordered set of 3D balls. By construction, the skin is constrained to be C-1 continuous, and for each ball, it is tangent to the ball along a circle of contact. Using an energy formulation, we derive differential equations that are designed to minimize the skin's surface area, mean curvature, or convex combination of both. Given an initial skin, we update the skin's parametric representation using the differential equations until convergence occurs. We demonstrate the method's usefulness in generating interpolating skins of balls of different sizes and in various configurations

3D ball skinning using PDEs for generation of smooth tubular surfaces

We present an approach to compute a smooth, interpolating skin of an ordered set of 3D balls. By construction, the skin is constrained to be C1 continuous, and for each ball, it is tangent to the ball along a circle of contact. Using an energy formulation, we derive differential equations that are designed to minimize the skin’s surface area, mean curvature, or convex combination of both. Given an initial skin, we update the skin’s parametric representation using the differential equations until convergence occurs. We demonstrate the method’s usefulness in generating interpolating skins of balls of different sizes and in various configurations

Variational skinning of an ordered set of discrete 2D balls

This paper considers the problem of computing an interpolating envelope of an ordered set of 2D balls. By construction, the envelope is constrained to be C1 continuous, and for each ball, it touches the ball at a point and is tangent to the ball at the point of contact. Using an energy formulation, we derive differential equations that are designed to minimize the envelope’s arc length and/or curvature subject to these constraints. Given an initial envelope, we update the envelope’s parameters using the differential equations until convergence occurs. We demonstrate the method’s usefulness in generating interpolating envelopes of balls of different sizes and in various configurations

Endovaskuler müdahalelerde x-ray videodan kılavuz teli izleme = Guidewire tracking in x-ray videos of endovascular interventions

Bu bildiride kalp x-ray videolarında kılavuz telinin izlenmesi ic¸in yeni bir metot sunulmaktadır. Değgişimler hesabı kullanılarak bir kobra eğrisini içkin ve dıştan gelen kuvvetler ile kısıtlayarak deforme eden türevsel denklemler türetilmiştir. Bu denklemler kullanılarak eğrinin güncellenmesi ile imgedeki kılavuz teline uygunluğu, pürüzsüzlüğü, ve telin uzunluğunun korunması sağlanır. Analitik olarak türettiğimiz bu denklemler önceki metotlardan farklı olarak teğetsel terimler de içermektedir. X-ray videolarda tipik olarak karşılaşılan zayıf kontrasta karşı imgeye bağlı öznitelik olarak faz eşlenmesi haritası kullanılmıs¸tır. Geliştirilen metodun başarısı deneysel sonuçlar ile düşük kontrastlı x-ray videoları ¨uzerinde kılavuz teli izleme ile gösterilmis¸tir

Shape-driven segmentation of the arterial wall in intravascular ultrasound images

Segmentation of arterial wall boundaries from intravascular images is an important problem for many applications in the study of plaque characteristics, mechanical properties of the arterial wall, its 3D reconstruction, and its measurements such as lumen size, lumen radius, and wall radius. We present a shape-driven approach to segmentation of the arterial wall from intravascular ultrasound images in the rectangular domain. In a properly built shape space using training data, we constrain the lumen and media-adventitia contours to a smooth, closed geometry, which increases the segmentation quality without any tradeoff with a regularizer term. In addition to a shape prior, we utilize an intensity prior through a non-parametric probability density based image energy, with global image measurements rather than pointwise measurements used in previous methods. Furthermore, a detection step is included to address the challenges introduced to the segmentation process by side branches and calcifications. All these features greatly enhance our segmentation method. The tests of our algorithm on a large dataset demonstrate the effectiveness of our approach

Shape-driven segmentation of the arterial wall in intravascular ultrasound images

Segmentation of arterial wall boundaries from intravascular images is an important problem for many applications in the study of plaque characteristics, mechanical properties of the arterial wall, its 3D reconstruction, and its measurements such as lumen size, lumen radius, and wall radius. We present a shape-driven approach to segmentation of the arterial wall from intravascular ultrasound images in the rectangular domain. In a properly built shape space using training data, we constrain the lumen and media-adventitia contours to a smooth, closed geometry, which increases the segmentation quality without any tradeoff with a regularizer term. In addition to a shape prior, we utilize an intensity prior through a non-parametric probability density based image energy, with global image measurements rather than pointwise measurements used in previous methods. Furthermore, a detection step is included to address the challenges introduced to the segmentation process by side branches and calcifications. All these features greatly enhance our segmentation method. The tests of our algorithm on a large dataset demonstrate the effectiveness of our approach

A robust and efficient approach to detect 3D rectal tubes from CT colonography

Purpose: The rectal tube (RT) is a common source of false positives (FPs) in computer-aided detection (CAD) systems for CT colonography. A robust and efficient detection of RT can improve CAD performance by eliminating such “obvious” FPs and increase radiologists’ confidence in CAD. Methods: In this paper, we present a novel and robust bottom-up approach to detect the RT. Probabilistic models, trained using kernel density estimation on simple low-level features, are employed to rank and select the most likely RT tube candidate on each axial slice. Then, a shape model, robustly estimated using Random Sample Consensus (RANSAC), infers the global RT path from the selected local detections. Subimages around the RT path are projected into a subspace formed from training subimages of the RT. A quadratic discriminant analysis (QDA) provides a classification of a subimage as RT or non-RT based on the projection. Finally, a bottom-top clustering method is proposed to merge the classification predictions together to locate the tip position of the RT. Results: Our method is validated using a diverse database, including data from five hospitals. On a testing data with 21 patients (42 volumes), 99.5% of annotated RT paths have been successfully detected. Evaluated with CAD, 98.4% of FPs caused by the RT have been detected and removed without any loss of sensitivity. Conclusion: The proposed method demonstrates a high detection rate of the RT path, and when tested in a CAD system, reduces FPs caused by the RT without the loss of sensitivity

Statistical Region Based Segmentation of Ultrasound Images

Segmentation of ultrasound images is a challenging problem due to speckle, which corrupts the image and can result in weak or missing image boundaries, poor signal to noise ratio, and diminished contrast resolution. Speckle is a random interference pattern that is characterized by an asymmetric distribution as well as significant spatial correla- tion. These attributes of speckle are challenging to model in a segmentation approach, so many previous ultrasound segmentation methods simplify the problem by assuming that the speckle is white and/or Gaussian distributed. Unlike these methods, in this paper we present an ultrasound-specific segmentation approach that addresses both the spatial correlation of the data as well as its intensity distribution. We first decorrelate the image and then apply a region-based active contour whose motion is derived from an appropri- ate parametric distribution for maximum likelihood image segmentation. We consider zero-mean complex Gaussian, Rayleigh, and Fisher-Tippett flows, which are designed to model fully formed speckle in the in-phase/quadrature (IQ), envelope detected, and display (log compressed) images, respectively. We present experimental results demon- strating the effectiveness of our method, and compare the results to other parametric and non-parametric active contours