Journal article
Scale-adjusted distance transform and its applications to segmentation of multimodal images
Methods (San Diego, Calif.), Vol.245, pp.55-68
01/2026
DOI: 10.1016/j.ymeth.2025.11.003
PMID: 41207402
Abstract
Distance transform (DT) is widely used for structural analysis of multi-dimensional (mainly 2-D and 3-D) objects. Association of DT values with local structure scale, often, adds challenges and limits the scopes of applications of DT in relative structural analysis among multiple objects with varying scales. In this paper, we introduce a new notion of scale-adjusted distance transform (SADT), conceptually different from traditional DT, which is independent of object scale and offers DT values of scale varying objects on a uniform scale with the value of ‘1’ at ridges. It has been shown that scale-adjusted distance is a metric function in a continuous Euclidean space, and SADT generates a normalized field that is invariant under translation, rotation, and isotropic scaling. The computational method for digital objects traces gradient flow paths on a conventional DT field and uses the change in velocity along a digital path to detect local ridges, which are then used to generate a scale-adjusted density (SAD) field. Finally, SADT is computed using the SAD value. The results of applying the method on 2-D and 3-D multimodal image datasets are presented. Two real life applications of SADT are shown: 1) segmentation of conjoined nuclei from 2-D microscopic images, and 2) multi-scale separation of conjoined artery-vein in 3-D pulmonary CT image of a pig lung phantom. SADT outperforms the traditional marker-controlled watershed algorithm in conjoined nuclei segmentation from 2D images and achieves highly accurate multi-scale artery–vein separation in the pig lung phantom experiment. The performance of SADT is invariant of image dimension and imaging modality. Unlike modern deep learning methods, the proposed fuzzy method is transparent and data modality independent. The source code and sample data are freely available at: https://github.com/CMATERJU-BIOINFO/Scale-Adjusted-Distance-Transform
•A novel scale-adjusted distance transform (SADT) has been proposed.•An algorithm is presented for the estimation of SADT in digital space.•SADT is applied for detecting object core and multiscale segmentation of conjoined objects.•SADT successfully segments conjoined nuclei in 2-D microscopic cell images.•SADT is also applied for conjoined pulmonary A/V separation from 3D lung CT images.•The proposed SADT method is independent of image dimension and modality.•Unlike modern deep learning systems, the proposed fuzzy method is transparent.
Details
- Title: Subtitle
- Scale-adjusted distance transform and its applications to segmentation of multimodal images
- Creators
- Nirmal Das - Department of AIML, Netaji Subhas Engineering College, Kolkata, IndiaSubhadip Basu - Jadavpur UniversityPunam K. Saha - University of Iowa
- Resource Type
- Journal article
- Publication Details
- Methods (San Diego, Calif.), Vol.245, pp.55-68
- DOI
- 10.1016/j.ymeth.2025.11.003
- PMID
- 41207402
- NLM abbreviation
- Methods
- ISSN
- 1046-2023
- eISSN
- 1095-9130
- Publisher
- Elsevier Inc
- Grant note
- CMATER Laboratory, Jadavpur UniversityUniversity of IOWA
Authors have no conflict of interest. The authors would like to thank CMATER Laboratory, Jadavpur University and University of IOWA for supporting this work. S.B. acknowledges the Science and Engineering Research Board grant (SUR/2022/002903), Government of India.
- Language
- English
- Electronic publication date
- 11/07/2025
- Date published
- 01/2026
- Academic Unit
- Electrical and Computer Engineering
- Record Identifier
- 9985027353202771
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