A real-time detection and positioning method for small and weak targets using a 1D morphology-based approach in 2D images

A small and weak target detection method is proposed in this work that outperforms all other methods in terms of real-time capability. It is the first time that two-dimensional (2D) images are processed using only one-dimensional1D structuring elements in a morphology-based approach, enabling the real-time hardware implementation of the whole image processing method. A parallel image readout and processing structure is introduced to achieve an ultra-low latency time on the order of nanoseconds, and a hyper-frame resolution in the time domain can be achieved by combining the row-by-row structure and the electrical rolling shutter technique. Experimental results suggest that the expected target can be successfully detected under various interferences with an accuracy of 0.1 pixels (1σ) under the worst sky night test condition and that a centroiding precision of better than 0.03 pixels (1σ) can be reached for static tests. The real-time detection method with high robustness and accuracy is attractive for application to all types of real-time small target detection systems, such as medical imaging, infrared surveillance, and target measurement and tracking, where an ultra-high processing speed is required.


Note 1. ERS based velocity determination in PIV
Assuming that (xi, yi) and (x0, y0) are centroid positions of particle Pi at the moment Ti and T0, respectively, as shown in Figure 1(b2), the velocity of particle Pi at the moment Ti could be determined by Equations (S1) and (S2): where and are the velocity of Pi at the moment Ti in horizontal direction and vertical direction, respectively.

Note 2. Small target simulation based on PSF model
A two-dimentional Gaussian distribution model based on Equation (3) is employed for a target spot simulation and the simulated target has a typical size of 5×5 pixels without background noise, as shown in Figure S1.

Figure S1
A simulated target with a typical size of 5×5 pixels and no background noise: (a) energy distribution; (b) the simulated image.
Note 3. FFT results of 1D targets with different sizes Figure S2 FFT results of 1D targets with different sizes.
When performing FFT on 1D objects, with the decrease in target scale, the spectrum in the frequency domain expands from low frequency to high frequency, which is consistent with the FFT results on 2D objects. As shown in the Figure S2, a sharp peak at the low frequency corresponds to a larger scale 1D target (Figure 2(c1)) while a broader distribution over a wide frequency range corresponds to a smaller scale 1D target ( Figure 2(c2)).

Note 4. Illustration of the 1D image processing approach with target recovery
After a threshold is applied to fulfil the image segmentation with all pixels brighter than the threshold value labeled as 1 and others labeled as 0, the erosion of the binarized image by a pair SE in both x and y directions could further remove single-point noise effectively. Targets with more than one valid pixel connected to each other could survive after the erosion. By comparing the results with (Figures 3(b) and (e)) or without erosion ( Figures S3(b) and (c)), more than 90 false targets have been eliminated after the erosion. Since part of the targets could also be eroded by aforementioned denoise processing, the target recovery method is introduced in Figure S4. After the OR-operation of two images processed by the erosion-dilation in two directions, the target keeps intact while single-point noise could be removed.     #For pixel output in 8 bits, storage space is expressed as depth×8 bits; for data after binarization, buffer depth is expressed as depth×1 bits.

Note 6. Line length optimization for SE
Step 1 and step 2 in Figure 3 are background analysis for image enhancement. Since the background is subtracted from the original image in step 3, less useful information left in the background will contribute to a more accurate target segmentation and target centroid calculation. Simulations are conducted with the target center locates 0.3 pixel and 0.2 pixel away from the pixel center in x direction and y direction, respectively (dx=0.3 pixel, dy=0.2 pixel). The systematic error is corrected in the simulation results and the centroiding error induced by the line length of SE1 in step 1 with respect to the size of simulated target is illustrated in Figure S6.

Figure S6
Optimization of SE line length in step 1.
Since the erosion in step 1 happens in the x direction, it has a more significant influence on the target centroiding accuracy in x direction than that in y direction. It is noted that there will be no centroiding error in both x and y directions, if the line length of SE1 is larger than the diameter of the target spot. In other word, since the goal of the erosion in step 1 is to eliminate all the target information for a more accuracy background analysis, a SE with the line length larger than the target size could achieve the goal by removing the whole target and inducing no error when further subtracting the background from the original image. Similar to that, the positive target whose size in x direction is smaller than the line length of SE will be removed by the erosion, whereas the negative noise, such as a broken point on the CMOS image sensor whose size in x direction is smaller than the line length of SE will be removed by the dilation in step 2. However, in order to remove a positive object with the size much larger than the line length of SE utilized in erosion, such as the moon, the line length of SE for dilation should not be smaller than that for erosion. Figure S7 illustrates the image processing results with different line length (L) of the SEs in steps 1 and 2. With a smaller L, the bigger and brighter non-target object (the moon) could be completely removed since the combination of the erosion and dilation could keep such object intact as background which will be subtracted from the original image, while its edge could not be removed effectively with a bigger L. However, some desired small targets could not be recognized when L is too small because any target with the scale smaller than L will be eliminated during erosion and the number of extracted targets will decrease with smaller L until L is smaller than any desired targets.