在近幾年來，QR碼被廣泛的應用在各式各樣的商品，以及隨著智慧型手機的相機功能及運算能力的增強，這使得與QR碼相關的技術快速成長，其中以QR碼影像的處理顯得極為重要。
本論文是探討當QR碼被覆貼在彎曲表面的物品或是印製在球面的商品上，再使用智慧型手機拍攝QR影像，此時手機所獲取的影像再也不是正規的QR碼，而是由於相機取像的角度與商品表面彎曲所造成的扭曲的QR碼影像，這種扭曲的QR影像將導致解碼失敗，因此本論文就是試著處理這樣的問題。
由於QR碼的設計是由黑白方塊所組成的影像，這些方塊被稱作模組(module)，本論文嘗試將球面上QR影像的模組透過曲線區分出來，將變形QR碼中每一模組的顏色(黑或白)填回至對應的空白矩陣位置，即可將扭曲的QR影像回正至標準的QR碼。此方法主要的目標為模擬出這些切割QR影像的線條，我們將這些線條用圓錐曲線近似，並稱此法為圓錐切割法。本研究將圓錐切割法分為兩類，第一類是由位置偵測圖示的邊緣進行切割，第二類則是將QR影像內部的角落點分群，再使用圓錐曲線擬合(conic fitting)將分群的角落點近似成圓錐曲線，在整張QR影像切割好後，即可校正回標準QR碼以進行解碼。依據上述的方法，我們可以成功地解碼許多嚴重扭曲的QR影像。

In recent years, QR code is widely used in various scenarios and environments. Due to the common use of smart phone and the enhancement of camera capability, applications related to QR codes grow fast. Therefore, the processing of the QR code images become an important task.
The thesis discusses the situation when QR codes are posted on curved surfaces or printed on spherical products. While taking picture of this kind of QR code, the image captured is no longer a standard QR code. Some kind of distortion can occur and we call the captured image as a “QR image”. In this thesis, our main purpose is to rectify QR image and decode it successfully.
QR code is constructed by black and white squares, which are called “module”. This thesis tries to generate curved lines which separate each module on QR image. After having those segmentation lines, we can map each module’s color (black or white) back to single block of square template. Then the QR image can be rectified to standard QR code. The key point of the thesis is to generate those curves. We use conic section to approximate those curves and we call this method “conic segmentation”.
The method we mentioned can be separated into two parts. First, we use the edges of position detection pattern and reflection conic fitting (referred to as RCF) to generate first eight segmentation lines in both horizontal and vertical direction. The second part of conic segmentation is to find QR image corners which belong to the same curve by calculating corner to curve distance. We fit those corners to conic curve. In this part, we use previous conic curve to predict next possible conic curve. After doing conic segmentation, it is easy to rectify QR image back to standard QR code. By using the proposed method, we can decode lots of severely distorted QR images.

[1] “Information technology-automatic identification and data capture techniques-bar code symbology-qr code,” Jun 2000.
[2] X. Li, Z. Shi, D. Guo, S. He, “Reconstruct Argorithm of 2D Barcode for Reading the QR Code on Cylindrical Surface,” Proc. IEEE Int. Conf. Anti-Counterfeiting, Security and Identification, Vol. 1, pp 1-5, Oct. 2013
[3] C. H. Chu, D. N. Yang, Y. L. Pan, and M. S. Chen, “Stabilization and Extraction of 2D Barcodes for Camera Phones,” ACM Multimedia System Journal, Vol. 17, No. 2, pp. 113-133, Mar. 2011.
[4] Z. L. Liao, T. L. Huang, R. Wang, X. Y. Zhou, “A Method of Image Analysis for QR code Recognition,” Proc. IEEE Int. Conf. Intelligent Computing and Integrated Systems, Vol.1, pp.250 – 253 ,Oct. 2010
[5] Jiejing Zhou, Yunfei Liu, P. Li, “Research on Binarization of QR code Image,” Proc. IEEE Int. Conf. Multimedia Technology, Vol.1, pp.1 – 4, Oct. 2010
[6] Nobuyuki Otsu, “A threshold selection method from gray-level histograms,” Proc. IEEETrans. Sys., Man., Cyber.Vol.9, pp. 62 –66, Jan 1979
[7] Irwin Sobel, “History and Definition of the Sobel Operator,” 2014
[8] Kolman, Bernard,Hill, David R., “Elementary Linear Algebra with Applications (9th ed.),”Prentice Hall,May, 2007
[9] C. Harris and M. Stephens, “A combined corner and edge detector,” Proceedings of the 4th Alvey Vision Conference. pp. 147–151, 1988
[10] Gonzalez, R.C. and Woods R.E., “Digital Image Processing, 3rd Edition,” Prentice-Hall, 2008.
[11] Hartshorne, Robin, “Foundations of Projective Geometry, 2nd ed.” Ishi Press, 2009
[12] 林鈺勛, “使用圓錐切割法將柱面上的QR碼影像回正,” 國立台灣科技大學電子工程研究所, 2014。