By B-mode (x-axis direction) and C-mode (y-axis direction) pseudo-scanning the Air Force target at the remote site, we have obtained its en face
) by slicing the volumetric image as shown in
. We can clearly see the structure of the arrayed fibers as well as the element bar patterns of the sample target. This pixelization limits the resolution and the contrast of the image [25
]. The corresponding 2-D magnitude of the discrete Fourier transform (DFT) is shown in and the peak frequency spacing (~20,000m−1
) matches to the spatial spacing of the periodically-spaced fiber cores (~50µm), which could be understood as a reciprocal space or a lattice in a crystalline solid [39
Obtained original unprocessed OCT en face image of US Air Force target: (a) original image with fiber pixelation effect; (b) Magnitude of 2-D discrete Fourier transform of the image.
After analyzing the histogram or intensity distribution of the original unprocessed image in , we have observed that the most of the pixel values are distributed in the lower region of the available gray levels (L=256 or 0-255 levels) as shown in
. The histogram equalization transfer function,
, which is the CDF of the original image is shown in the inset as well. We then fully mapped all the gray scale values of the original image to the full range of gray levels, i.e., 0-255, in our experiments. This is very useful since the relatively small signal obtained by OCT can be effectively enhanced or brightened without losing any of the original information. By applying histogram equalization to the raw image, we can highlight the image from lower gray scales by increasing the scale levels as shown in . In this case, in addition to the enhanced intensities for the image patterns, the relatively low intensity backgrounds are also enhanced. After enhancing the image contrast, we eliminated the pixelation of the fiber bundle by applying Gaussian smoothing filter with 19×19 window and σ=5 pixels to obtain the intended final image as shown in
. Due to the pre-enhancement using the histogram equalization, we were able to observe element numbers and the bars clearly without presence of any fiber pixelization effect. In addition, other structural features such as larger scratches represented by darker patterns pointed out by arrows as well as damaged fiber pixels became clearly visible. illustrates the changes in the histogram of the processed image (red dotted line) compared to the original image (blue solid line), where it has moved from the narrow lower range to a moderate scale level with a broader width. For finite image histogram, we can further improve the image contrast by clipping histogram edges below 50 and/or above 200 so that additional contrast stretching can be achieved without image deformation.
Results of histogram equalization method: (a) histogram distribution (probability) of the raw image with gray scale level (inset: corresponding transfer function of the histogram equalization); (b) USAF chart image after histogram equalization.
Fig. 5 Gaussian smoothing filtered result with a pre histogram equalized image: (a) USAF chart image with combined histogram equalization and Gaussian weighted filter; (b) histogram comparison between before (blue solid line) and after (red dotted line) image (more ...)
Meanwhile, as in Ref [9
], using Gaussian smoothing filter without applying the histogram enhancement method can also remove the fiber pixelization effect as presented in
using our original OCT image (). In , the resultant histogram of the processed image experiences minimal change due to the weighted averaging effect. However, the image histogram is still concentrated rather in the lower gray scale range (centered at its average scale value) which is not ideal for differentiating the details when it is displayed compared to our combined method containing the histogram equalization method. Furthermore, we have lost (at least for a human viewer) some of other surface features of the fiber by applying smoothing filter which averaged or blended the image information as well as reduced the intensity level by half (the image is darker than the original one). Those features were obvious in our result in . Here, we should mention that applying additional histogram technique after this Gaussian filter deteriorates the image because this enhances the already averaged gray scale values of the backgrounds and the signal patterns which make it difficult to differentiate each other. In our work, we have successfully demonstrated that by inserting the histogram equalization as a pre-process before applying the Gaussian smoothing filter, we could obtain clear and detail features in the OCT image after Gaussian filtering. This would be preferred for real tissue imaging having less abrupt edges compared to that in the USAF chart. In this case, the edge blurring effect can be ignored if the size of fiber pixel is relatively smaller than the sample pattern. Otherwise, the image resolution is limited by fiber pixel dimension so that finer pixel size is required to appropriately image the sample/pattern. The edge blurring can also be compensated by applying other de-blurring or image segmentation algorithms if needed [40
Fig. 6 Image result after applying Gaussian smoothing filter only: (a) chart image after Gaussian filtering; (b) corresponding histogram of the processed image (original image: blue solid line; processed image: black dotted line). Inset figure: spatial frequency (more ...)
In terms of spatial frequencies, i.e., magnitude of the Fourier transform of the image [see
], we have observed that the histogram equalization sharpens the side lobes (black dashed line) by adjusting contrast of the image. However, we have also observed that the high frequency components created by the periodic spacing of the fibers are suppressed by Gaussian smoothing filter (red dotted line) which acts as a low pass filter, resulting in the side lobe reduction by 40.99dB (marked with a red arrow: the spectral density is squared to the FFT magnitude). In comparison, there is no significant difference taking only smoothing filter without histogram equalization. In addition, the figures of merit for images such as contrast (marked with black square) and the CNR (marked with blue circle) are shown in . Image contrast is defined as,
is the mean pixel value of the object (patterns) region and
is the mean pixel value of the background (no pattern) region. The corresponding CNR of the image is computed by,
is the standard deviation of the noise in the background region. After the histogram equalization, both the contrast and the CNR slightly decreased because not only the gray scale values of the background (
) but also the background noise variation (
) increased. However, the Gaussian low pass filter decreases the background variation which improved the CNR by more than 13dB and 9.8dB enhancement for the histogram equalized image and for the unprocessed raw original image, respectively, with minimum change to the image contrast.
Fig. 7 Comparison in characteristics of the image: (a) magnitude of Fourier transforms (blue solid line for original image; black dashed line for histogram equalized image; red dotted line for Gaussian smoothing filtered image with pre-histogram equalization); (more ...)
The effect of the Gaussian filter width and window size on the image quality is compared in
where the image contrast varies less than 0.5dB () no matter what filter parameters are used whereas the CNR enhancement was dependent on those parameters in . If the filter width is less than 3 pixels, the processed image, even after Gaussian smoothing, still contains the fiber pixel effect. For larger filter dimensions and width, the images were blurred too much and lost the sharpness of the bar patterns and the small surface features of the bundle. This result matches well when one consider the data sampling rate of each image pixel (
: 5µm) with the fiber core spacing (~50µm). Therefore, to decouple the honey-comb effect of the fiber grid, the smoothing filter should cover the whole fiber core with significant mask coefficients at least for each core area, which is represented by filter parameters, size and width, of the Gaussian smoothing filter. Thus, the optimized conditions for the filter parameters in our case for achieving the pixel removal with minimum image deformation (distinctive features incorporated in the original image) are
. The inset in shows the histogram of the resultant images for
where there is no significant change observable in the histogram distribution.
Comparison in image qualities of Gaussian filtered image with various filter parameters (filter size, m, and filter width, σ) post the histogram equalization: (a) image contrast; (b) image CNR.
The detailed mapping image results are shown in
for comparison where each row represents for filter width
and each column for filter size m
= 11,15,19,23,27, respectively. Essentially those parameters of the image filters should be considered based on several conditions for optimization: size of fiber core, separation of adjacent cores, number of image pixels dedicated to a single fiber core, and the dimension of a sample object. Thus, the full width of the Gaussian filter (
) was set to cover the entire core spacing in the fiber bundle [9
]. In our case, the filter width (σ
), pixel distance, and the core spacing were 5, 5, and 50 respectively. The optimized mask size of the filter was found based on the analysis result in . Thus, the selected combination for filter parameters was
in our experiment as presented in . The filtered images, however, should be carefully compared because the figure of merits could be greater even though there still remains fiber bundle artifact. For further quantitative evaluation of the image quality with different filter parameters, one may use alternative image quality metrics such as mean square error (MSE), provided that there exists a reference image,
, that does not have fiber bundle artifact. For each filtered output image,
, the MSE can be computed as [41
Because we do not have a clean reference image that does not have fiber bundle artifact, CNR and image contrast (C) are compared before and after image processing [42
Since there was no lens on the sample side of the bundle, and using a relatively high NA (0.53) fiber, the imaging depth was approximately ~500µm from the end of the fiber bundle. Therefore, the pixelation effect was different at different depths for thick samples which we did not address in this work. However, the purpose of this preliminary work was to study the effectiveness of the method in eliminating the pixelation effect in an en face OCT image based on a fiber bundle imager. By doing so, we were able to compare other previous results utilizing the fiber bundle imager and present the effectiveness of our proposed method. In this case, as an advantage, we can set a rather symmetrical image kernel that can be applied for both directions in the image plane. However, image processing for a depth-resolved 2-D image should be dealt in a different way because it lacks the symmetry between the lateral (B-mode) and axial (A-mode) directions in the acquired image. For a 3-D (including C-mode) volumetric image, the same 2-D plane mask that we used in this work can be applied at different depth layers so that all the possible en face image in different depths construct the whole 3-D volume image. For a 2-D cross-sectional (B-mode) image, the filter mask should be reduced to a 1-D line to process each depth layer line by line because there is no relationship between lateral and depth scanning directions. Our current work was rather a study targeted for a 2-D en face image incorporating only lateral dimensions at the target surface which can clearly visualize the fiber arrangement artifact as the SEM image in . This proposed image processing method can be extended for different imaging dimensions such as 3-D volumetric and 2-D cross-sectional images.