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標題: 使用形態學方法於改善投影機銳利度量測之研究
A Study on The Improvement of Sharpness Measurement for Projectors Using The Morphological Approach
作者: 陳怡如 
Yi-Ju Chen 
關鍵字: 巴特沃夫凹陷濾波器;高斯凹陷濾波器;低通濾波器;灰階形態學;Butterworth notch filter;Gaussian notch filter;Low pass filter;gray-level morphology
引用: [1] D. Williams, 'What is an MTF... and why should you care?,' RLG DigiNews, vol. 2, no. 1, 1998. [2] Imatest. (2018). Sharpness: What is it and how is it measured?|imatest. Available: [3] O. I. d. Normalización, ISO 12233: 2000, Photography--Electronic Still Picture Cameras--Resolution Measurements. International Organization for Standardization, 2000. [4] R. C. Gonzalez and R. E. Woods, 'Digital image processing second edition,' Beijing: Publishing House of Electronics Industry, vol. 455, 2002. [5] E. Amraei and M. Mobasheri, 'STRIPING NOISE REMOVAL OF IMAGES ACQUIRED BY CBERS 2 CCD CAMERA SENSOR,' International Archives of the Photogrammetry, Remote Sensing & Spatial Information Sciences, 2014. [6] P. Moallemi and M. Behnampourii, 'Adaptive Optimum Notch Filter for Periodic Noise Reduction in Digital Images,' (in en), AUT Journal of Electrical Engineering, vol. 42, no. 1, pp. 1-7, 04/01 2010. [7] Z. Ji, H. Liao, X. Zhang, and Q. Wu, 'Simple and efficient soft morphological filter in periodic noise reduction,' in TENCON 2006. 2006 IEEE Region 10 Conference, 2006, pp. 1-4: IEEE. [8] N. Otsu, 'A threshold selection method from gray-level histograms,' IEEE transactions on systems, man, and cybernetics, vol. 9, no. 1, pp. 62-66, 1979. [9] G. Matheron and J. Serra, 'The birth of mathematical morphology,' in Proc. 6th Intl. Symp. Mathematical Morphology, 2002, pp. 1-16: Sydney, Australia. [10] J. P. B. R. C. Gonzalez, J. M. R. C. Gonzalez, Ed. Advances in Image Analysis (Introduction to Binary Morphology). SPIE Press, Bellingham, Wash., 1992. [11] J. P. B. R. C. Gonzalez, J. M. R. C. Gonzalez, Ed. Advances in Image Analysis (Introduction to Gray-Scale Morphology). SPIE Press, Bellingham, Wash., 1992. [12] J. Lee, R. Haralick, and L. Shapiro, 'Morphologic edge detection,' IEEE Journal on Robotics and Automation, vol. 3, no. 2, pp. 142-156, 1987. [13] P. Maragos and R. Schafer, 'Morphological skeleton representation and coding of binary images,' IEEE Transactions on Acoustics, Speech, and Signal Processing, vol. 34, no. 5, pp. 1228-1244, 1986. [14] B.-K. Jang and R. T. Chin, 'Analysis of thinning algorithms using mathematical morphology,' IEEE Transactions on pattern analysis and machine intelligence, vol. 12, no. 6, pp. 541-551, 1990. [15] D. Shaked and A. M. Bruckstein, 'Pruning medial axes,' Computer vision and image understanding, vol. 69, no. 2, pp. 156-169, 1998.
銳利度量測(Sharpness measurement)是鏡頭在出廠前的重要基本指標,一台鏡頭是否可以拍攝出清晰的影像,取決於此。目前也已經有相當成熟的方法,可以利用影像處理的方式進行量測,在這裡,我們希望可以將此方法也應用在光學投影機上面。在進行鏡頭量測時,會需要高解析度的圖紙進行拍攝並量測,但因為投影機投出的影像本身品質並不能如同圖紙一般平滑,基於此條件,在量測之前需要對測試影像進行改善,利於後續量測。

在對影像進行改善的前提條件是不可以影響量測出來的數據,因此我們針對量測方法進行解析,發現量測方法中最重要的資訊來自於斜邊影像的邊界資料,而投影機影像的不平滑現象來自於投影面板的像素排列,因此影像看起來彷彿被週期訊雜訊影響,因此前期利用了頻率域濾波器,如:巴特沃夫凹陷濾波器(Butterworth notch filter)、高斯凹陷濾波器(Gaussian notch filter)、低通濾波器(Low pass filter)…等方法進行實驗,發現除了將雜訊去除之外,有些濾波器會有振鈴(Ringing)現象,且在去除頻率雜訊時,同時也將邊界影像的資訊去除了,導致量測出來的結果不理想。既然邊界資料不能受到影響,為了解決這個問題,我們利用灰階形態學(Gray-level morphology)和Otsu法將影像進行分割,個別處理邊界區域,以及不平滑的區域,以獲得可用來量測的測試影像。實驗結果顯示所提的方法可以保留足夠的邊界資料,並且抹平測試影像不平滑的部分,進而得到相對正確的銳利度量測資料。

Sharpness measurement is an important basic indicator of the lens before leaving the factory. Whether a lens can capture a clear image depends on this. At present, there is already quite mature method for measuring sharpness using image processing. Here, we want to use this method for optical projectors. When performing lens measurement, high-resolution charts are required for shooting and measurement, but because the image quality of the projector is not as smooth as the chart, based on this condition, we need to improve the test image before measurement, which is conducive to subsequent measurement.

The precondition for improving the image is that it cannot affect the measured result. Therefore, we analyze the measurement method and find that the most important information in the measurement method comes from the boundary data of the slanted-edge image. The image of the projector is not smooth because of the pixel arrangement of the panel. Therefore, the image seems to be affected by periodic noise. Therefore, in the early stages, we used frequency domain filters to eliminate noises, such as: Butterworth notch filter, Gaussian notch filter, Low pass filter, etc. However, some filters detect ringing after noise reduction. When the noise is removed, the information in the boundary is also deleted. The result is not satisfied. Since the boundary data cannot be affected, in order to solve this problem, we use gray-level morphology and Otsu method to segment the image and process the boundary and non-smooth regions separately to obtain a test image that can be used for measurement. Experimental results show that the proposed method can preserve enough boundary data and smooth the non-smooth regions of the test image to obtain relatively accurate sharpness measurement result.
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