Position Detection of a Scattering 3D Object by Use of the Axially Distributed Image Sensing Technique
 Author: Cho Myungjin, Shin Donghak, Lee JoonJae
 Organization: Cho Myungjin; Shin Donghak; Lee JoonJae
 Publish: Journal of the Optical Society of Korea Volume 18, Issue4, p414~418, 25 Aug 2014

ABSTRACT
In this paper, we present a method to detect the position of a 3D object in scattering media by using the axially distributed sensing (ADS) method. Due to the scattering noise of the elemental images recorded by the ADS method, we apply a statistical image processing algorithm where the scattering elemental images are converted into scatterreduced ones. With the scatterreduced elemental images, we reconstruct the 3D images using the digital reconstruction algorithm based on ray backprojection. The reconstructed images are used for the position detection of a 3D object in the scattering medium. We perform the preliminary experiments and present experimental results.

KEYWORD
Axially distributed image sensing , Threedimensional detection , Scattering medium

I. INTRODUCTION
Visualization and detection of a 3D object in optically scattering media is a challenging problem. An improved visualization method of scattered images can be applied to various applications such as imaging in fog, underwater, security, and medical diagnostics [17]. Some 3D multiperspective approaches including integral imaging and axially distributed sensing (ADS) have been studied for visualizing objects in the scattering media [89]. Among them, the ADS scheme can provide simple recording architecture by translating a camera along its optical axis. The recorded highresolution elemental images generate the clear 3D plane images for the partially occluded 3D objects.
In this paper, we present a position detection method for a 3D object in scattering media by using the ADS method [1012]. In the proposed method, we introduce the statistical signal processing to reduce the scattering effect in elemental images and the position detection process with nonlinear correlation operation is newly applied to the scattered images in ADS. The proposed method is divided into four parts: (1) pickup (2) statistical image processing (3) digital reconstruction and (4) position detection. In the pickup part using the ADS method, the camera is moved along a common optical axis and multiple longitudinal 2D images of the scene are recorded. The recorded multiple 2D images of the 3D object in the scattering media are referred to as scattering elemental images. In the second statistical processing part, to reduce the scattering effects of the recorded elemental images, a statistical image processing technique is applied to the scattering elemental images. Then, the statistically processed elemental images are used to reconstruct the 3D plane images using the digital reconstruction algorithm based on ray backprojection in the third part. In the final part, the reconstructed plane images are used for 3D object detection. To show the feasibility of the proposed method, we carry out the preliminary experiments for a scattering 3D object behind a diffuser screen as the scattering medium.
II. RECOGNITION METHOD USING ADS
2.1. Pickup Method in ADS
The pickup part of the ADS method is shown in Fig. 1. We translate a single camera along the optical axis and record multiple 2D images of the scene observed through the scattering media. We suppose that the object is located at a distance
z_{0} from the 1st camera position. The distance between the cameras is Δz. We recordK elemental images by moving the camera. The first camera isk =1 atz_{k} =z_{0} and the camera closest to the object becomes byk =K atz_{k} =z_{0} (K 1)Δz . Due to the different distance from the object for each camera, the object is recorded in each elemental image with a different magnification. Each magnification ratio is calculated asM_{k} =z_{k} /g whereg is the focal length of the camera.2.2. Statistical Processing of Elemental Images
When a 3D object is located in scattering media, the recorded image may contain severe scattering noise which can prevent the correct visualization and detection for the 3D object. In this paper, therefore, we wish to reduce the noise by using statistical image processing. To do so, we apply statistical image processing techniques to the scattering elemental images. Let us assume that degradation caused by the diffuser can be modeled as Gaussian [6]. The statistical image processing procedure to reduce the scattering effect in the elemental images is shown in Fig. 2. First, we estimate the unknown parameter
μ (mean) of theGaussian distribution using theMaximum Likelihood Estimation (MLE). Here we consider that the scattering degradation function is composed of many superimposed Gaussian random variables with local area (w_{x} ×w_{y} ) of an elemental image with (N_{x} ×N_{y} ) pixels. Let us denote these random variables asX_{ij} (m ,n ). Then, MLE is calculated bywhere
L (··) is the likelihood function,i =1, 2, ⋯,N_{x} −w_{x} +1,j =1, 2, ⋯,N_{y} −w_{y} +1,m =1, 2, ⋯,w_{x} , andn =1, 2, ⋯,w_{y} . And, the mean parameter of theGaussian distribution is estimated asThe estimated elemental images are obtained by subtracting . The estimated elemental images are given by
This estimation process enables us to reduce the scattering noise in the elemental images.
Gamma (γ ) correction is then used for the estimated elemental images. UsingGamma correction, we can manipulate the histogram to improve the contrast ratio [8]. Gamma correction is a nonlinear method to control the overall luminance of a still image. Gamma correction is typically used to adjust still images for accurate reproduction on physical displays. In this case, it is used to compensate for the nonlinear relationship between pixel values and the intensity being displayed. Therefore, for the estimated elemental images, it may be expressed by the following powerlaw relationship:where
S_{uncorrected} andS_{corrected} are the uncorrected and corrected elemental images respectively, andγ is the gamma value.Next, we apply histogram equalization and matching to the corrected elemental images. This process can remove artificial gray levels from the elemental images. We first calculate a cumulative distribution function (CDF) and this is given by
where
h ,h_{e} , andq are continuous gray levels of the histogram stretched image, the histogram equalized image, and histogram matched image.p_{h} (w ) andp_{q} (t ) are the continuous probability density functions corresponding to the h’s and q, andw andt are the integration variables. Equations (5) and (6) should be followed byG (q ) =T (h ) where the inverse of theG operation yields the restored image. Finally, we can obtain the new scatterreduced elemental images.2.3. Digital Reconstruction in ADS
In the proposed method, the third part is the digital reconstruction using the scatterreduced elemental images. This is shown in Fig. 3. It is based on ray backpropagation through virtual pinholes. This reconstruction algorithm numerically implements the reverse of the pickup process. In other words, all scatterreduced elemental images are back projected and magnified by different magnifications
M_{k} (z ) if the reconstruction plane is located atz . The magnified scatterreduced elemental images are superimposed at the same reconstruction plane. Finally, we can obtain the reconstructed plane image at distancez . Then, the reconstructed plane imager (x, y, z ) is the summation of all the magnified elemental imagesS_{k} and is given byFor faster calculation, the reconstruction process may be normalized by the magnification ratio
M_{1} . This becomes2.4. Position Detection Process
In the last part of the proposed method, the plane image
r (x, y, z ) reconstructed atz distance from the digital reconstruction part is used for 3D object position detection. When a plane image of the target object is reconstructed atz distance, correlation is performed with the reference imagef to detect the position of the 3D object. The reference image can become a clear object image without scattering medium. Then, we simply obtain the correlation peak result from nonlinear correlation operation as given bywhere
α is the nonlinear parameter and means the strength of the applied nonlinearity. In general, the choice ofα depends on the type of noise and object [14]. It could vary within the range [0, 1].F andR are the Fourier transforms off andr , respectively. Andϕ_{F} andϕ_{R} represent the phase angle off andr , respectively. In Eq. (9), the correlation peak indicates the position detection performance between the reference image and the reconstructed plane image.III. EXPERIMENTS AND RESULTS
To demonstrate the proposed position detection method for a 3D object in scattering media, we carried out optical experiments. The experimental setup is shown in Fig. 4 where a ‘car’ object is positioned approximately 440 mm away from the first camera position. We placed a diffuser at approximately 50 mm in front of the object. The thickness of the diffuser was 1 mm. We used a camera with 2184×1456 pixels with 8.2 um pixel pitch. An imaging lens with focal length
g =70 mm was used. We used the camera with the smallest aperture to obtain the maximum depth of field. Then, the pinhole gap (g ) becomes 70 mm in the digital reconstructions as shown in Fig. 3. The camera is moved with a step of 5 mm and a total ofK =41 elemental images are recorded within a total displacement distance of 200 mm. The first elemental image and the 41st elemental image are shown in Fig. 4(c) and 4(d), respectively. We can see that the recorded elemental images were degraded by the scattering noise.To reduce the scattering noise in the elemental images, the statistical image processing technique was applied to them as described in Fig. 3. Figure 5 shows the example of the 21st elemental image produced by the statistical image processing technique. The 21st elemental image shown in Fig. 5(a) was scatterreduced as shown in Fig. 5(b). The statistical image processing was repeated to all the recorded elemental images. Then, we can obtain the 41 scatterreduced elemental images.
To reconstruct the 3D images, the scatterreduced 41 elemental images were computationally back projected through virtual pinholes according to Eq. (8). The 3D plane images were obtained according to the reconstruction distance. Some reconstructed plane images are shown in Fig. 6(a) for three different reconstruction distances (340 mm, 440 mm, and 540 mm). When the distance of reconstruction plane was 440 mm, where the ‘car’ object is originally located, the reconstructed image is well focused after reducing the scattering noises through the statistical image processing. For comparison, the plane images are shown in Fig. 6(b) when using the conventional method without the statistical image processing.
To detect the position of the 3D object, the nonlinear correlation operation as described in Eq. (9) was used for the original reference image and the reconstructed plane images. The correlation peak results are shown in Fig. 7 according to the reconstruction distances from 340 mm to 540 mm. Here the nonlinear parameter was 0.6. We can see that the correlation peaks are very low in the conventional method. This is because all of the reconstructed plane images have heavily scattered noise regardless of the reconstruction distance. On the other hand, we can see the highest correlation peak at 440 mm where the object was originally located in the result of the proposed method. At the original position of the object, the 2D correlation output was shown in Fig. 8(a) when the original image and our scatterreduced plane image were used. For comparison, the correlation output in the conventional method is very low when the scattered plane image was used as shown in Fig. 8(b). Figure 9 shows the graph of the maximum correlation peaks according to the nonlinear parameter (
α ) in Eq. (9). These results reveal that the scatterreduced plane image provides the higher position detection performance compared with the scattered plane image for allα values.IV. CONCLUSION
In conclusion, the ADSbased position detection method for a 3D object in scattering media was presented. The elemental images recorded by the ADS method contain severe scattering noise. To reduce the scattering noise, we applied a statistical image processing algorithm to the scattering elemental images. Thus, we were able to obtain the improved 3D plane images using the digital reconstruction algorithm based on ray backprojection. Using them, we compare the correlation performance for the proposed method and the conventional method. The experimental results reveal that the proposed method is superior to the conventional method in terms of correlation operation.

[FIG. 1.] Pickup part of ADS.

[FIG. 2.] Statistical image processing for the recorded elemental images.

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[FIG. 3.] Ray diagram for digital reconstruction.

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[FIG. 4.] (a) Original object (b) Experimental setup. (c) 1st scattering elemental image (d) 41st scattering elemental image.

[FIG. 5.] (a) ‘car’ image within 21st elemental image (b) Statistically processed images.

[FIG. 6.] Reconstructed plane images at different distances (a) Proposed method (b) Conventional method.

[FIG. 7.] Correlation peak results according to the reconstruction distance.

[FIG. 8.] Nonlinear correlation results when α=0.6 (a) Proposed method (b) Conventional method. x and y mean the pixel indexes of the correlation output.

[FIG. 9.] Nonlinear correlation results according to the α value.