H-SegMed: A Hybrid Method for Prostate Segmentation in TRUS Images via Improved Closed Principal Curve and Improved Enhanced Machine Learning

Abstract

Prostate segmentation is an important step in prostate volume estimation, multi-modal image registration, and patient-specific anatomical modeling for surgical planning and image-guided biopsy. Manual delineation of the prostate contour is time-consuming and prone to inter- and intra-observer variability. Accurate prostate segmentation in transrectal ultrasound images is particularly challenging due to the ambiguous boundary between the prostate and neighboring organs, the presence of shadow artifacts, heterogeneous intra-prostate image intensity, and inconsistent anatomical shapes. Therefore, in this study, we propose a novel hybrid segmentation method (H-SegMed) for accurate prostate segmentation in TRUS images. The method consists of two main steps: (1) an improved closed principal curve-based method was used to obtain the data sequence, in which only few radiologist-defined seed points were used as an approximate initialization; and (2) an enhanced machine learning method was used to achieve an accurate and smooth contour of the prostate. Our results show that the proposed model achieved superior segmentation performance compared with several other state-of-the-art models, achieving an average Dice similarity coefficient, Jaccard similarity coefficient (Ω), and accuracy of 96.5, 95.1, and 96.3%, respectively.

Appendix

Appendix table used symbols in this work

Used in the method	Description	Symbols
Global View	Temporary variables	s = 1,2,.,N
	Real number system	IR
	Raw data set	Data
	Each point in the Data set	Data = {p1,p2,..,ps}
	Number of points in Data set	N
	X-axis coordinate of each point	x
	Y-axis coordinate of each point	y
GCPC	Temporary variables	iv/jv = 1,2,..,num;is/js = 1,2,..,k ip = 1,2,..,N
	Principal curve	f
	Newly added vertex/ determined vertex in the principal curve	viv/vjv
	Number of vertices of principal curve	num
	Number of segments	k
	Length of segment	L
	Optimal weight of penalty factor	β
	Average squared distance	ΔN(fk,N)
	Maximum distance deviation	Δs
	Current Distance	CD
	Last Loop Distance	LLD
	Angle between two segments	α
	Data radius	R
	Distance from data point to principal curve	DSip
	Minimum/ Maximum distance from data point to principal curve	DSmin/ DSmax
	Data sequence	D = {d1,d2,..,dN}
	Projection index	t
	Execution time	ext
MADE	Temporary variables	z = 1,2,.,Pop
	Population size	Pop
	Population candidate	cz
	Lower/ upper bounds of the search space	Umin/Umax
	Present/ Maximum iteration number	G/ Gmax
	Mutation factor	F
	Crossover rate	CR
	Mutated individual	vz
	Trial individual	uz
	Length of chromosome	CS
	Mean mutation Factor	uF
	Mean Crossover Rate	uCR
	Set of all successful mutation factors	SF
	Set of all successful crossover probabilities	SCR
	Number of solutions	Np
	Probability of using the mutation operator	ProbG
	Maximal/minimal probability of using the mutation operator	Probmax/ Probmin
	Expression function	fun(•)
CFBT	Temporary variables	h = 1,2,.,n;i = 1,2,.,l; j = 1,2,.,m
	Neurons of input layer	Ih ∈ {I1, I2,…,In}
	Neurons of hidden layer	Hi ∈ {H1, H2, …, Hl}
	Neurons of output layer	Oj ∈ {O1, O2,…, Om}
	Input of input layer	$X^{s}$
	Input/output of hidden layer	${\text{H}}_{Ii}^{s}$/${\text{H}}_{Oi}^{s}$
	Input/output of output layer	${\text{Y}}_{Ij}^{s}$/${\text{Y}}_{j}^{s}$
	Weight from input layer to the hidden layer	w1hi
	Weight from hidden layer to the output layer	w2ij
	Thresholds of the i-th hidden neuron	ai
	Thresholds of the u-th output neuron	bj
	Activation functions from input to hidden layer	fun1(•)
	Activation functions from hidden to output layer	fun2(•)
	Construsted function	funj(•)
	Mean Square Error function	E
	Expected result	${\text{O}}_{j}^{s}$(equals to ps in this work)
	Caputo derivative operator	Caputo(•)
	Learning rate from input layer to the hidden layer	η1
	Learning rate from hidden layer to the output layer	η2
	Gammar function	$\Gamma$
	Objective sum function	g(•)
	Adjustment parameter	ap
	Training iteration number	r
Evaluation parameters	Dice Similarity Coefficient	DSC
	Jaccard Similarity Coefficient	Ω
	Accuracy	ACC
	True Positive	TP
	False Positive	FP
	False Negative	FN
	True Negative	TN