Hexagonal-Grid-Layout Image Segmentation Using Shock Filters: Computational Complexity Case Study for Microarray Image Analysis Related to Machine Learning Approaches
Abstract
:1. Introduction
1.1. Main Findings
- The image-processing workflow represents a general solution for both rectangular and hexagonal grid alignment, which has been successfully applied to both medical images and images of material structures.
- The shock-filter-based grid alignment also delivers segmentation information, and guided by an autocorrelation procedure, it estimates the locations of missing objects within the hexagonal grid layout.
- The computational complexity required to determine the grid layout is minimized, taking into account that the PDEs are targeting the one-dimensional luminance function profiles,
- The segmentation accuracy was evaluated by computing the means and standard deviations of distances between the annotated and detected centers and showed improved results compared with state-of-the-art research.
1.2. Shock-Filter Fundamentals
2. Shock-Filter-Based Approach for Microarray Image Segmentation
2.1. Materials and Methods
2.2. Preprocessing
2.3. Grid-Line Detection for Image Registration
2.4. Spot Segmentation
3. Results and Discussions
3.1. Microarray Image Registration and Segmentation Accuracy
3.2. Shock Filters as a General Approach for Hexagonal-Grid-Layout Registration
3.3. Computational Complexity Analysis for the Hexagonal-Grid-Layout Image Segmentation
- (i)
- The morphological opening procedure and the autocorrelation spot size estimation cost are given by the upper bound function , with s representing one computational step, and representing the size of the structural element used for morphological filtering.
- (ii)
- The computational complexity of the shock-filter-based procedure for grid alignment is based on the number of microarray spots found on each line and in each column of spots, denoted by and , respectively. Let d be the average of the microarray spot diameter and be the average width for a line or a column of spots. We computed for each spot line and spot column, the horizontal and vertical image profiles, respectively, with the total complexity of . Shock filters were applied to each of the determined profiles having a complexity of , where represents p iterations performed on the number of profiles (i.e., one profile for each line of spots), and each profile was of size M. This led to the estimation of the computational cost given by , with . Consequently, the order of growth for the total computational cost was approximated to , and it represents the total computational complexity of the proposed method.
Reference | Method | Cost Arguments | Order of Growth |
---|---|---|---|
[1,33] | Voronoi diagrams | S | |
[52] | Growing concentric hexagons | ||
[43,71] | Support vector machines | ||
[72] | Evolutionary algorithms | ||
[67,68] | Deep neural Networks | - | - |
present | Shock filters driven by morphology |
4. Conclusions
Author Contributions
Funding
Conflicts of Interest
References
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Exp. ID | ||||||
---|---|---|---|---|---|---|
FE18398 | 0.988 | 0.075 | 0.420 | 0.412 | ||
FE18399 | 0.993 | 0.029 | 0.395 | 0.406 | ||
FE18400 | 0.982 | 0.093 | 536 | 524 | 0.414 | 0.385 |
FE18401 | 0.994 | 0.046 | 0.392 | 0.397 |
Reference/ | Method Description | Image, Grid Type | Image Size / | Spot | Metric | Value |
---|---|---|---|---|---|---|
Dataset | Number of Spots | Diam. | ||||
SMD | Gridding based on support vector | Real, Rectangular grid | 1980 × 1917 | 10 | Mean | 2.52 |
[42,60] | machines and genetic algorithms | 9196 | Std | 2.59 | ||
Acc | 96.4 | |||||
Nycter | K-nearest neighbor | Synthetic, | 3188 × 9552 | 14 | Mean | 1.77 |
[61] | Rectangular grid | 576,756 | Std | 1.16 | ||
Acc | 98.9 | |||||
CNV370 | Voronoi diagrams | Real, Rectangular grid | 2800 × 2800 | 6 | Mean | 1.88 |
[52] | 9216 | Std | 0.82 | |||
Acc | 99.8 | |||||
Nycter | Gridding based on support vector | Real, Rectangular grid | 2800 × 2800 | 14 | Mean | 1.91 |
machines and genetic algorithms | 9216 | Std | 1.03 | |||
Acc | 99.3 | |||||
SMD | Voronoi diagrams | Real, Synthetic with | various sizes | 14 | Mean | 1.94 |
Nycter | rectangular and | Std | 2.32 | |||
[52] | hexagonal grids | Acc | 97.5 | |||
FEdata | Shock filter driven by mathematical | Real, Hexagonal | 1650 × 4320 | 14 | Mean | 1.52 |
(present) | morphology | 9196 | Std | 0.68 | ||
Acc | 100 |
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Baloi, A.; Costea, C.; Gutt, R.; Balacescu, O.; Turcu, F.; Belean, B. Hexagonal-Grid-Layout Image Segmentation Using Shock Filters: Computational Complexity Case Study for Microarray Image Analysis Related to Machine Learning Approaches. Sensors 2023, 23, 2582. https://doi.org/10.3390/s23052582
Baloi A, Costea C, Gutt R, Balacescu O, Turcu F, Belean B. Hexagonal-Grid-Layout Image Segmentation Using Shock Filters: Computational Complexity Case Study for Microarray Image Analysis Related to Machine Learning Approaches. Sensors. 2023; 23(5):2582. https://doi.org/10.3390/s23052582
Chicago/Turabian StyleBaloi, Aurel, Carmen Costea, Robert Gutt, Ovidiu Balacescu, Flaviu Turcu, and Bogdan Belean. 2023. "Hexagonal-Grid-Layout Image Segmentation Using Shock Filters: Computational Complexity Case Study for Microarray Image Analysis Related to Machine Learning Approaches" Sensors 23, no. 5: 2582. https://doi.org/10.3390/s23052582
APA StyleBaloi, A., Costea, C., Gutt, R., Balacescu, O., Turcu, F., & Belean, B. (2023). Hexagonal-Grid-Layout Image Segmentation Using Shock Filters: Computational Complexity Case Study for Microarray Image Analysis Related to Machine Learning Approaches. Sensors, 23(5), 2582. https://doi.org/10.3390/s23052582