A family of smooth and interpolatory basis functions for parametric curve and surface representation

IEEE Trans. on Image Process.

2018

Abstract-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) projectionbased 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.

Section: ) Learning Shape Priorsmentioning

confidence: 99%

Section: ) Classification In Medical Imagingmentioning

confidence: 99%

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

IEEE Trans. on Image Process.

2018

“…Parametric curves that are represented by compactly supported basis functions are often used to construct active-contour models [16], [17] and to segment bioimages [18]- [20]. More generally, the control-point-based nature of (4) makes this model particularly convenient in applications where user interaction is required [21], [22]. The reason is that the simple adjustment of one control point is enough to adjust the curve locally.…”

Section: A Periodic Signals and Closed Parametric Curvesmentioning

confidence: 99%

An Inner-Product Calculus for Periodic Functions and Curves

Badoual

IEEE Signal Process. Lett.

2016

Our motivation is the design of efficient algorithms to process closed curves represented by basis functions or wavelets. To that end, we introduce an inner-product calculus to evaluate correlations and L2 distances between such curves. In particular, we present formulas for the direct and exact evaluation of correlation matrices in the case of closed (i.e., periodic) parametric curves and periodic signals. We give simplifications for practical cases that involve B-splines. To illustrate this approach, we also propose a least-squares approximation scheme that is able to resample curves while minimizing aliasing artifacts. Another application is the exact calculation of the enclosed area.

“…is finite, and ' and are spline basis functions that satisfy the Riesz basis condition [8]. For the explicit expressions of ' and to construct a cylindrical surface, we refer the reader to [9].…”

Section: Spline-based Implementationmentioning

confidence: 99%

Closed-form alignment of active surface models using splines

2017 IEEE 14th International Symposium on Biomedical Imaging (ISBI 2017)

2017

We propose a new formulation of the active surface model in 3D. Instead of aligning a shape dictionary through the similarity transform, we consider more flexible affine transformations and introduce an alignment method that is unbiased in the sense that it implicitly constructs a common reference shape. Our formulation is expressed in the continuous domain and we provide an algorithm to exactly implement the framework using spline-based parametric surfaces. We test our model on real 3D MRI data. A comparison with the classical active shape model shows that our method allows us to capture shape variability in a dictionary in a more precise way.Index Terms-Active surface model, 3D, parametric surfaces, splines, continuous domain Fig. 1. Real data set consisting of 14 3D MRI scans. The red meshes outline the segmented descending thoracic aorta.