Table 3.

Object-wise metrics for testing (for gland objects). The reported values are average value $\pm \text{standard error}$ over the set of 37 images. ${\mathcal{S}}^{\text{pixel}}$: our method, ${\mathcal{S}}^{\text{Nguyen}}$: $k$-means clustering and nuclei–lumen association-based method by Nguyen et al.,²³ ${\mathcal{S}}^{\text{Naik}}$: active contour method by Naik et al.,¹⁷ and ${\mathcal{S}}^{\text{Farjam}}$: texture-based method by Farjam et al.¹⁶

Method	JI (${\mathrm{JI}}_{\text{weighted}}$)	DI (${\mathrm{DI}}_{\text{weighted}}$)	${\mathbf{U}}_{\mathcal{G}}$	${\mathbf{U}}_{\mathcal{S}}$	HD (${\mathrm{HD}}_{\text{weighted}}$)	Object matching $F$-score
${\mathcal{S}}^{\text{pixel}}$	$\mathbf{0}.\mathbf{54}\pm \mathbf{0}.\mathbf{01}$	$\mathbf{0}.\mathbf{65}\pm \mathbf{0}.\mathbf{01}$	$\mathbf{0}.\mathbf{04}\pm \mathbf{0}.\mathbf{006}$	$0.11\pm 0.02$	$189.98\pm 13.27$	$\mathbf{74}.\mathbf{54}\pm \mathbf{1}.\mathbf{42}$
${\mathcal{S}}^{\mathrm{Nguyen}}$	$0.38\pm 0.01$	$0.49\pm 0.01$	$0.10\pm 0.02$	$0.17\pm 0.01$	$\mathbf{177}.\mathbf{83}\pm \mathbf{13}.\mathbf{58}$	$58.24\pm 1.68$
${\mathcal{S}}^{\mathrm{Naik}}$	$0.26\pm 0.02$	$0.37\pm 0.03$	$0.20\pm 0.02$	$\mathbf{0}.\mathbf{02}\pm \mathbf{0}.\mathbf{002}$	$497.04\pm 57.47$	$51.26\pm 3.14$
${\mathcal{S}}^{\mathrm{Farjam}}$	$0.01\pm 0.0008$	$0.02\pm 0.0002$	$0.00\pm 0$	$0.12\pm 0.004$	$228.46\pm 14.55$	$1.101\pm 0.078$

Note: The best results are shown in bold.