From a Non-Local Ambrosio-Tortorelli Phase Field to a Randomized Part Hierarchy Tree

Genctav, Murat

doi:10.1007/s10851-013-0441-8

Cited by 19 publications

(10 citation statements)

References 33 publications

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“…As the screening parameter in (1.1) tends to ∞, the screened Poisson equation approaches to the Poisson equation. The controlled smoothing provided by the screening parameter is advocated by some researchers, and recent works [7,1,62,69,15,29] have rejuvenated the model.…”

Section: Our Contributionmentioning

confidence: 99%

“…Though this observation was made in the early work [70], the follow-up work on screened Poisson typically focused on isolated treatment of the ρ 2 . Rangarajan (see [62,23]) took a very small value to approximate the eikonal equation, while Tari (see [1,69]) and Shah [64] used very large values. We believe that isolated treatment is hindering full utilization of the controlled smoothing offered by the model.…”

Section: A 2d Scale Spacementioning

confidence: 99%

“…We believe that isolated treatment is hindering full utilization of the controlled smoothing offered by the model. As we show in section 4.2, once the entire scale space is utilized, both local and global interactions can be realized, and a natural hierarchical central-to-peripheral decomposition of the shape domain is achieved without requiring the recent nonlocal term in [69].…”

Section: A 2d Scale Spacementioning

confidence: 99%

“…In [6], smooth distance fields are considered as L p distance fields, where p is the control variable. A recent shape field related to the screened Poisson [69] is a fluctuating field consisting of both negative and positive values inside the shape by addition of a zero-mean constraint to the shape field. The zero level set then partitions the shape domain into two: one that corresponds to the central region, a coarse and compact shape, and one that corresponds to the peripheral region, which includes protrusions from a shape.…”

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confidence: 99%

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Screened Poisson Hyperfields for Shape Coding

Güler¹,

Ünal²

2014

SIAM J. Imaging Sci.

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We present a novel perspective on shape characterization using the screened Poisson equation. We discuss that the effect of the screening parameter is a change of measure of the underlying metric space. Screening also indicates a conditioned random walker biased by the choice of measure. A continuum of shape fields is created by varying the screening parameter or, equivalently, the bias of the random walker. In addition to creating a regional encoding of the diffusion with a different bias, we further break down the influence of boundary interactions by considering a number of independent random walks, each emanating from a certain boundary point, whose superposition yields the screened Poisson field. Probing the screened Poisson equation from these two complementary perspectives leads to a high-dimensional hyperfield: a rich characterization of the shape that encodes global, local, interior, and boundary interactions. To extract particular shape information as needed in a compact way from the hyperfield, we apply various decompositions either to unveil parts of a shape or parts of a boundary or to create consistent mappings. The latter technique involves lower-dimensional embeddings, which we call screened Poisson encoding maps (SPEM). The expressive power of the SPEM is demonstrated via illustrative experiments as well as a quantitative shape retrieval experiment over a public benchmark database on which the SPEM method shows a high-ranking performance among the existing state-of-the-art shape retrieval methods.

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Section: Our Contributionmentioning

confidence: 99%

Section: A 2d Scale Spacementioning

confidence: 99%

Section: A 2d Scale Spacementioning

confidence: 99%

mentioning

confidence: 99%

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Screened Poisson Hyperfields for Shape Coding

Güler¹,

Ünal²

2014

SIAM J. Imaging Sci.

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“…The phase field of Ambrosio and Tortorelli (AT) [5] providing a continuous indicator for the boundary/nonboundary state at every image point has been used by a number of applications in variational image and shape analysis, [39], [9], [44], [24], [30], [36], [43]. In addition to segmentation and restoration applications, AT-based features are recently proposed for coding shape parts [42], serving as a bridge between the high level process of shape abstraction and low level processes of smoothing and edge detection. To deal with noise and visual transformations, the partitioning is stored in a hierarchical tree with probabilistic structure.…”

Section: Introductionmentioning

confidence: 99%