Sparsification Scale-Spaces

Cárdenas, M. C.; Peter, Pascal; Weickert, Joachim

doi:10.1007/978-3-030-22368-7_24

Cited by 3 publications

(14 citation statements)

References 20 publications

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“…Multiple different Lyapunov sequences can be specified that emphasise specific types of simplification. In analogy to sparsification scale spaces [3], for J = {1, ..., N }, we can use the total image contrast…”

Section: Property 4: Lyapunov Sequencesmentioning

confidence: 99%

“…Moreover, it is invariant under any brightness rescaling operations that keep the histogram, and thus the level sets, intact. Now that the important properties of quantisation scale-spaces have been verified, we briefly compare them to their spatial relatives, the sparsification scale-spaces [3]. Then, in Section 4, we also consider practical applications for this novel type of scale-space.…”

Section: Property 5 (Invariances)mentioning

confidence: 99%

“…Sparsification scale-spaces [3] rely on a series of nested inpainting masks that specify known data for an image with domain Ω with |Ω| = N . They start with a full mask K 0 = Ω and successively reduce K to K +1 by removing exactly one pixel coordinate from this set.…”

Section: Relations To Sparsification Scale-spacesmentioning

confidence: 99%

“…While there are many viable choices for A, we only consider homogeneous diffusion inpainting [8] here, where A corresponds to a finite difference discretisation of the Laplacian with reflecting boundary conditions. For more details on sparsification scale-spaces we refer to Cárdenas et al [3]. Both sparsification and quantisation scale-spaces have a discrete scale parameter.…”

Section: Relations To Sparsification Scale-spacesmentioning

confidence: 99%

“…Image inpainting [11] reconstructs an image from a mask that specifies known pixel data at a subset of all image coordinates. Cárdenas et al [3] have shown that a wide variety of inpainting operators can create scale-spaces: Sequentially removing points from the mask yields inpainting results that form a scale-space with the mask density as a discrete scale dimension. The order in which the data is removed, the sparsification path, can impact the reconstruction quality significantly.…”

Section: Introductionmentioning

confidence: 99%

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Quantisation Scale-Spaces

Peter¹

2021

Preprint

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Recently, sparsification scale-spaces have been obtained as a sequence of inpainted images by gradually removing known image data. Thus, these scale-spaces rely on spatial sparsity. In the present paper, we show that sparsification of the co-domain, the set of admissible grey values, also constitutes scale-spaces with induced hierarchical quantisation techniques. These quantisation scale-spaces are closely tied to information theoretical measures for coding cost, and therefore particularly interesting for inpainting-based compression. Based on this observation, we propose a sparsification algorithm for the grey-value domain that outperforms uniform quantisation as well as classical clustering approaches.

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Section: Property 4: Lyapunov Sequencesmentioning

confidence: 99%

Section: Property 5 (Invariances)mentioning

confidence: 99%

Section: Relations To Sparsification Scale-spacesmentioning

confidence: 99%

Section: Relations To Sparsification Scale-spacesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Quantisation Scale-Spaces

Peter¹

2021

Preprint

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Quantisation Scale-Spaces

Peter

2021

Lecture Notes in Computer Science

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Probabilistic diffusion models excel at sampling new images from learned distributions. Originally motivated by drift-diffusion concepts from physics, they apply image perturbations such as noise and blur in a forward process that results in a tractable probability distribution. A corresponding learned reverse process generates images and can be conditioned on side information, which leads to a wide variety of practical applications. Most of the research focus currently lies on practice-oriented extensions. In contrast, the theoretical background remains largely unexplored, in particular the relations to drift-diffusion. In order to shed light on these connections to classical image filtering, we propose a generalised scale-space theory for probabilistic diffusion models. Moreover, we show conceptual and empirical connections to diffusion and osmosis filters.

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Generalised Diffusion Probabilistic Scale-Spaces

Peter

2024

J Math Imaging Vis

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Diffusion probabilistic models excel at sampling new images from learned distributions. Originally motivated by drift-diffusion concepts from physics, they apply image perturbations such as noise and blur in a forward process that results in a tractable probability distribution. A corresponding learned reverse process generates images and can be conditioned on side information, which leads to a wide variety of practical applications. Most of the research focus currently lies on practice-oriented extensions. In contrast, the theoretical background remains largely unexplored, in particular the relations to drift-diffusion. In order to shed light on these connections to classical image filtering, we propose a generalised scale-space theory for diffusion probabilistic models. Moreover, we show conceptual and empirical connections to diffusion and osmosis filters.

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Sparsification Scale-Spaces

Cited by 3 publications

References 20 publications

Quantisation Scale-Spaces

Quantisation Scale-Spaces

Quantisation Scale-Spaces

Generalised Diffusion Probabilistic Scale-Spaces

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