Persistent homology for object segmentation in multidimensional grayscale images

Assaf, Rabih; Goupil, Alban; Vrabie, Valériu; Boudier, Thomas; Kacim, Mohammad

doi:10.1016/j.patrec.2018.08.007

Cited by 16 publications

(13 citation statements)

References 16 publications

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“…The occurrence of topological anomalies associated with smoothing operations is well understood in the field of image segmentation (e.g., [70][71][72][73]). Various enhanced image-segmentation techniques have been proposed in order to ameliorate such problems, like homology-based preservation techniques [74][75][76][77][78][79][80], topology-derivative-based techniques [81][82][83][84][85], and adaptive refinement techniques [72,[86][87][88][89][90][91].…”

Section: Introductionmentioning

confidence: 99%

Topology-preserving scan-based immersed isogeometric analysis

Divi

Verhoosel

Auricchio

et al. 2022

Computer Methods in Applied Mechanics and Engineering

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Section: Introductionmentioning

confidence: 99%

Topology-preserving scan-based immersed isogeometric analysis

Divi

Verhoosel

Auricchio

et al. 2022

Computer Methods in Applied Mechanics and Engineering

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“…The first type of method for TIM we consider is image smoothing . Note that this method has previously been used in conjuction with persistent homology of images 5 . However, its true potential within the context of TIM remained unnoticed.…”

Section: Methodsmentioning

confidence: 99%

“…For the past decade, persistent homology 1 -the most prominently used and studied tool within the field of Topological Data Analysis (TDA) 2 -has lead to many new applications for image segmentation and classification [3][4][5][6][7][8] . The great potential of TDA for images is due to their grid-like structure.…”

Section: Topological Image Modification For Object Detection and Topomentioning

confidence: 99%

“…Our current work builds upon the idea that persistent homology can be used to detect objects in images 5 . However, many real-world images contain outliers, as well as irrelevant objects, which complicate the use of persistent homology for this purpose.…”

Section: Introductionmentioning

confidence: 99%

“…Unlike existing TDA methods for object detection or segmentation, through TIM and TIP we are able to discard significant but irrelevant objects 5 , 7 , which is the main purpose for which we designed this method. Furthermore, although we will consider skin lesion images for illustrating the effectiveness of our method, we do not require any specific textural assumptions restricted to this domain 7 .…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Topological image modification for object detection and topological image processing of skin lesions

Vandaele

Nervo²,

Gevaert

2020

Sci Rep

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We propose a new method based on Topological Data Analysis (TDA) consisting of Topological Image Modification (TIM) and Topological Image Processing (TIP) for object detection. Through this newly introduced method, we artificially destruct irrelevant objects, and construct new objects with known topological properties in irrelevant regions of an image. This ensures that we are able to identify the important objects in relevant regions of the image. We do this by means of persistent homology, which allows us to simultaneously select appropriate thresholds, as well as the objects corresponding to these thresholds, and separate them from the noisy background of an image. This leads to a new image, processed in a completely unsupervised manner, from which one may more efficiently extract important objects. We demonstrate the usefulness of this proposed method for topological image processing through a case-study of unsupervised segmentation of the ISIC 2018 skin lesion images. Code for this project is available on https://bitbucket.org/ghentdatascience/topimgprocess.

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2D+t track detection via relative persistent homology

Assaf

Goupil

Rammal

et al. 2020

Int J Imaging Syst Tech

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In this paper, we demonstrate that algebraic topology can be used to perform 2D+t object detection. After the construction of a topological complex for a 2D+t image sequence, we build a nested sequence of cell complexes on which relative persistent homology is computed. The relative homology adds to “absolute” homology the computation of classes related to the first and last frames of the sequence. By identifying 2D chains with large life spans, the most persistent classes are extracted. This allows for the identification of the interesting parts in a sequence and for the detection of the movement of objects despite continuous deformations in the image domain. The results obtained on a synthetic image and on two real biomedical images with moving vesicles recorded by a quantitative phase time‐lapse technique show the potential of this method. Comparing the method with a newly developed tracking tool proves that the strength of this method is its independence from prior parameters.

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Persistent homology for object segmentation in multidimensional grayscale images

Cited by 16 publications

References 16 publications

Topology-preserving scan-based immersed isogeometric analysis

Topology-preserving scan-based immersed isogeometric analysis

Topological image modification for object detection and topological image processing of skin lesions

2D+t track detection via relative persistent homology

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