Implementation of a real-time star centroid extraction algorithm with high speed and superior denoising ability

Jianqun Ding; Dongkai Dai; Wenfeng Tan; Xingshu Wang; Shiqiao Qin

doi:10.1364/AO.450502

Applied Optics
Vol. 61,
Issue 11,
pp. 3115-3122
(2022)
•https://doi.org/10.1364/AO.450502

Implementation of a real-time star centroid extraction algorithm with high speed and superior denoising ability

Jianqun Ding, Dongkai Dai, Wenfeng Tan, Xingshu Wang, and Shiqiao Qin

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Jianqun Ding, Dongkai Dai, Wenfeng Tan, Xingshu Wang, and Shiqiao Qin, "Implementation of a real-time star centroid extraction algorithm with high speed and superior denoising ability," Appl. Opt. 61, 3115-3122 (2022)

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Abstract

Star tracker is the most precise attitude measuring device, and its advantages include a high resolution and high update rate. Star centroid extraction, which is a very time-consuming process, has great influence on the attitude update rate. This paper proposes a real-time star centroid extraction algorithm based on a field programmable gate array. First, a 1D top-hat filter is used for star segmentation, which is suitable for both uniform and nonuniform background conditions. Second, multichannel image data is reorganized together into a complete frame through image stitching, which prevents the star spots on the channel boundary from being divided into different parts. Finally, star coordinates are extracted by the center-of-mass algorithm. For an image sensor with a resolution of $2048 \times 2048$ pixels, simulation results conducted by a ModelSim simulator show that the star centroid processing time of a single frame is roughly 5.2 ms. Real night experiments demonstrate that the standard deviation of a star centroid error is within ${10^{- 2}}$ pixel and the standard deviation of attitude is (2.6 2.2 12.0) arcseconds, which proves that the proposed star centroid extraction algorithm can work continuously and stably.

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Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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If ROI current label is not over then
$\sum x * f (x, y) [label_current]$	$<= x * f (x, y) + \sum x * f (x, y) [label_current] + \sum x * f (x, y) [label_up_pixel]$
$\sum y * f (x, y) [label_current]$	$<= y * f (x, y) + \sum y * f (x, y) [label_current] + \sum y * f (x, y) [label_up_pixel]$
$\sum f (x, y) [label_current]$	$<= f (x, y) + \sum f (x, y) [label_current] + \sum f (x, y) [label_up_pixel]$
$\sum pixel_counter [label_current]$	$<= 1 + \sum pixel_c o u n t e r [label_current] + \sum pixel_counter [label_up_pixel]$
$\sum x * f (x, y) [label_up_pixel]$	$<= 0$
$\sum y * f (x, y) [label_up_pixel]$	$<= 0$
$\sum f (x, y) [label_up_pixel]$	$<= 0$
$\sum pixel_counter [label_up_pixel]$	$<= 0$
$\sum x * f (x, y)$	$<= 0$
$\sum y * f (x, y)$	$<= 0$
$\sum f (x, y)$	$<= 0$
$pixel_counter$	$<= 0$
else if ROI current label is over then
$l a b e l_c u r r e n t <= (l a b e l_c u r r e n t < max_l a b e l_n u m) ? (l a b e l_c u r r e n t + 1) : 8^{'} d l;$
if ROI centroid extraction is over & $p i x e l_min < p i x e l_c o u n t e r < p i x e l_max$ then
$\sum x * f (x, y)$	$<= \sum x * f (x, y) [l a b e l_current]$
$\sum y * f (x, y) [label_up_pixel]$	$<= \sum y * f (x, y) [label_current]$
$\sum f (x, y) [label_up_pixel]$	$<= \sum f (x, y) [label_current]$
$pixel_counter$	$<= \sum pixel_counter [label_current]$
else ROI is not a star point then
$\sum x * f (x, y)$	$<= 0$
$\sum y * f (x, y)$	$<= 0$
$\sum f (x, y)$	$<= 0$
$pixel_counter$	$<= 0$

Matlab Extraction Results	FPGA Extraction Results
X/(pixel)	Y/(pixel)	X/(pixel)	Y/(pixel)
416.1881	1513.1314	416.1232	1513.1823
493.9705	1587.3049	493.9249	1587.2385
504.9694	1411.7054	504.9314	1411.653
561.9989	1895.0687	562.0920	1895.1258
…	…	…	…
1996.2353	1242.6845	1996.3075	1242.6015

Methods	Resource	Utilization	Available	Utilization (%)
Star extraction with image stitching	Slice LUTs	8361	20800	40.2%
	Slice registers	10527	41600	25.3%
	Block RAM	6	50	12%
	DSPs	25	90	27.8%
Four-channel direct star extraction	Slice LUTs	11301	20800	54.3%
	Slice registers	12498	41600	30%
	Block RAM	4	50	8%
	DSPs	80	90	88.9%

Parameter	Value	Parameter	Value
FPGA	XC7A35T-2FGG484	Pixel size	$5.5 µ m \times 5.5 µ m$
Image sensor	CMV4000-3E12M1PP	Resolution	$2048 \times 2048$ pixels
Chroma	Monochromatic	Focal length	35 mm
Bit depth	12 bits	Field of view	$18^{\circ} \times 18^{\circ}$
Exposure mode	External	Exposure time	200 ms

If ROI current label is not over then
$\sum x * f (x, y) [label_current]$	$<= x * f (x, y) + \sum x * f (x, y) [label_current] + \sum x * f (x, y) [label_up_pixel]$
$\sum y * f (x, y) [label_current]$	$<= y * f (x, y) + \sum y * f (x, y) [label_current] + \sum y * f (x, y) [label_up_pixel]$
$\sum f (x, y) [label_current]$	$<= f (x, y) + \sum f (x, y) [label_current] + \sum f (x, y) [label_up_pixel]$
$\sum pixel_counter [label_current]$	$<= 1 + \sum pixel_c o u n t e r [label_current] + \sum pixel_counter [label_up_pixel]$
$\sum x * f (x, y) [label_up_pixel]$	$<= 0$
$\sum y * f (x, y) [label_up_pixel]$	$<= 0$
$\sum f (x, y) [label_up_pixel]$	$<= 0$
$\sum pixel_counter [label_up_pixel]$	$<= 0$
$\sum x * f (x, y)$	$<= 0$
$\sum y * f (x, y)$	$<= 0$
$\sum f (x, y)$	$<= 0$
$pixel_counter$	$<= 0$
else if ROI current label is over then
$l a b e l_c u r r e n t <= (l a b e l_c u r r e n t < max_l a b e l_n u m) ? (l a b e l_c u r r e n t + 1) : 8^{'} d l;$
if ROI centroid extraction is over & $p i x e l_min < p i x e l_c o u n t e r < p i x e l_max$ then
$\sum x * f (x, y)$	$<= \sum x * f (x, y) [l a b e l_current]$
$\sum y * f (x, y) [label_up_pixel]$	$<= \sum y * f (x, y) [label_current]$
$\sum f (x, y) [label_up_pixel]$	$<= \sum f (x, y) [label_current]$
$pixel_counter$	$<= \sum pixel_counter [label_current]$
else ROI is not a star point then
$\sum x * f (x, y)$	$<= 0$
$\sum y * f (x, y)$	$<= 0$
$\sum f (x, y)$	$<= 0$
$pixel_counter$	$<= 0$

Abstract

Data availability

Cited By

Figures (8)

Tables (5)

Equations (13)

Applied Optics