Multiresolution Subdivision Snakes

We present a new active contour to segment cell aggregates. We describe it by a smooth tessellation that is attracted toward the cell membranes. Our approach relies on subdivision schemes that are tightly linked to the theory of wavelets. The shape is encoded by control points grouped in tiles. The smooth and continuously defined boundary of each tile is generated by recursively applying a refinement process to its control points. We deform the smooth tessellation in a global manner using a ridge-based energy that we have designed for that purpose. By construction, cells are segmented without overlap and the tessellation structure is maintained even on dim membranes. Leakage, which afflicts usual image-processing methods (e.g., watershed), is thus prevented. We validate our framework on both synthetic and real microscopy images, showing that the proposed method is robust to membrane gaps and to high levels of noise.

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“…where ↑ 2 k denotes an upsampling by a factor of 17], and h is the subdivision mask whose z-transform is…”

Section: Closed Subdivision Curvesmentioning

confidence: 99%

“…Parametric active contours-a.k.a. snakes-are popular models for the interactive segmentation of bioimages [13][14][15][16][17]. They consist in a curve that evolves from an initial position toward the boundary of the object of interest through the minimization of an energy term [16,18].…”

Section: Introductionmentioning

confidence: 99%

Deforming Tessellations For The Segmentation Of Cell Aggregates

Badoual

Galan

Sage

et al. 2019

2019 IEEE 16th International Symposium on Biomedical Imaging (ISBI 2019)

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“…In fact, a standard computational approach to signal processing is to extend by periodization the signals of otherwise bounded support. Periodic signals arise also naturally in applications such as the parametric representation of closed curves [14]- [16]. This has motivated the development of signal-processing tools and techniques specialized to periodic signals in sampling theory, error analysis, wavelets, stochastic modelization, or curve representation [17]- [23].…”

Section: Periodic and General Settingmentioning

confidence: 99%

Periodic Splines and Gaussian Processes for the Resolution of Linear Inverse Problems

Badoual

Fageot

Unser

2018

IEEE Trans. Signal Process.

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This paper deals with the resolution of inverse problems in a periodic setting or, in other terms, the reconstruction of periodic continuous-domain signals from their noisy measurements. We focus on two reconstruction paradigms: variational and statistical. In the variational approach, the reconstructed signal is solution to an optimization problem that establishes a tradeoff between fidelity to the data and smoothness conditions via a quadratic regularization associated to a linear operator. In the statistical approach, the signal is modeled as a stationary random process defined from a Gaussian white noise and a whitening operator; one then looks for the optimal estimator in the mean-square sense. We give a generic form of the reconstructed signals for both approaches, allowing for a rigorous comparison of the two. We fully characterize the conditions under which the two formulations yield the same solution, which is a periodic spline in the case of sampling measurements. We also show that this equivalence between the two approaches remains valid on simulations for a broad class of problems. This extends the practical range of applicability of the variational method.

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“…Proposition 4 describes the refinement scheme and provides the corresponding convergence result. where ↑ m denotes upsampling by a factor m as defined in (21). Then, the iterative scheme is convergent, in the sense that…”

Section: Modified Refinement Scheme Based On Exponential B-splinesmentioning

confidence: 99%

“…Shapemodeling frameworks that allow for user interaction can usually be categorized in either discrete or continuous-domain models. Discrete models are typically based on interpolating polygon meshes or subdivision [16,17,18,19,20,21] and they easily allow to locally refine a shape. Subdivision models are also considered as hybrids between discrete and continous-domain models because they iteratively define continuous functions in the limit.…”

Section: Introductionmentioning

confidence: 99%

Compactly-supported smooth interpolators for shape modeling with varying resolution

et al. 2017

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A B S T R A C TIn applications that involve interactive curve and surface modeling, the intuitive manipulation of shapes is crucial. For instance, user interaction is facilitated if a geometrical object can be manipulated through control points that interpolate the shape itself. Additionally, models for shape representation often need to provide local shape control and they need to be able to reproduce common shape primitives such as ellipsoids, spheres, cylinders, or tori. We present a general framework to construct families of compactly-supported interpolators that are piecewise-exponential polynomial. They can be designed to satisfy regularity constraints of any order and they enable one to build parametric deformable shape models by suitable linear combinations of interpolators. They allow to change the resolution of shapes based on the refinability of B-splines. We illustrate their use on examples to construct shape models that involve curves and surfaces with applications to interactive modeling and character design.

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Multiresolution Subdivision Snakes

Cited by 24 publications

References 47 publications

Deforming Tessellations For The Segmentation Of Cell Aggregates

Deforming Tessellations For The Segmentation Of Cell Aggregates

Periodic Splines and Gaussian Processes for the Resolution of Linear Inverse Problems

Compactly-supported smooth interpolators for shape modeling with varying resolution

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