【摘要】：隨著現(xiàn)代教育技術(shù)和人工智能技術(shù)的迅速發(fā)展,對(duì)學(xué)科題目機(jī)器解答的研究再一次變得火熱起來(lái)。相較于其他學(xué)科,數(shù)學(xué)是一門以數(shù)量和關(guān)系為基礎(chǔ)的學(xué)科,研究數(shù)學(xué)題目的機(jī)器解答是研究機(jī)器解答技術(shù)的一個(gè)很好的切入點(diǎn)。本文為了幫助實(shí)現(xiàn)平面幾何題目的機(jī)器解答,對(duì)題目平面幾何圖像中實(shí)體信息的抽取和表示問(wèn)題進(jìn)行了研究。針對(duì)幾何實(shí)體檢測(cè)過(guò)程中遇到的圖形重疊結(jié)構(gòu)、虛線等情況,根據(jù)平面幾何圖像的特點(diǎn),有針對(duì)地測(cè)試了實(shí)體檢測(cè)的相關(guān)算法,并提出了多種后期優(yōu)化處理策略,實(shí)現(xiàn)了較為魯棒的實(shí)體檢測(cè)流程和較高的檢測(cè)精度。并隨后從檢測(cè)結(jié)果中抽取出了幾何實(shí)體的有用信息,這些信息既可以通過(guò)一致化表示作為結(jié)果直接展示,幫助學(xué)生理解并自主探索題目的解答,又可以和文本信息整合,得到題目更為完整的信息,幫助實(shí)現(xiàn)平面幾何題目的機(jī)器解答。本文研究?jī)?nèi)容主要包括兩個(gè)部分。第一個(gè)部分是幾何實(shí)體的檢測(cè)部分,主要包括圖像預(yù)處理、幾何實(shí)體檢測(cè)和檢測(cè)優(yōu)化三個(gè)步驟。通過(guò)實(shí)驗(yàn)分析與比較,本文選取自適應(yīng)高斯核二值化算法對(duì)平面幾何圖像進(jìn)行二值化,并對(duì)二值化后的圖像進(jìn)行8-連通域標(biāo)記,以分割出相應(yīng)的平面幾何圖形區(qū)域和標(biāo)識(shí)字符區(qū)域。對(duì)于其中的平面幾何圖形區(qū)域,首先利用RANSAC圓檢測(cè)方法對(duì)圓實(shí)體進(jìn)行檢測(cè),并在檢測(cè)后消除圖像中圓實(shí)體的相關(guān)像素點(diǎn),然后用漸進(jìn)概率霍夫變換進(jìn)行線段實(shí)體的檢測(cè),最后再通過(guò)大量的后期優(yōu)化處理以保證更為魯棒的檢測(cè)效果,包括連通域標(biāo)記優(yōu)化、虛線的檢測(cè)與恢復(fù)等,得到所有幾何實(shí)體基于坐標(biāo)系統(tǒng)的原始信息。第二部分是幾何實(shí)體信息的抽取與表示部分,主要包括標(biāo)識(shí)字符的OCR、實(shí)體信息抽取、實(shí)體信息表示三個(gè)步驟。其中對(duì)標(biāo)識(shí)字符區(qū)域的OCR過(guò)程使用BP神經(jīng)網(wǎng)絡(luò)進(jìn)行訓(xùn)練識(shí)別,并把對(duì)應(yīng)的標(biāo)識(shí)字符結(jié)果整合到離當(dāng)前字符區(qū)域中心距離最近的點(diǎn)實(shí)體的屬性信息中。同時(shí),總結(jié)了平面幾何圖像中有效的實(shí)體信息類型,并給出了基于坐標(biāo)系統(tǒng)的對(duì)應(yīng)抽取方法。最后,根據(jù)所抽取到的實(shí)體信息使用謂詞擴(kuò)展表示形式、方程系統(tǒng)表示形式、自然語(yǔ)言表示形式三種方式進(jìn)行一致化表示。本文最終形成了一個(gè)魯棒的幾何實(shí)體信息抽取與表示的統(tǒng)一框架,并在收集的圖像數(shù)據(jù)集上進(jìn)行了大量實(shí)驗(yàn),對(duì)該框架的合理性與魯棒性進(jìn)行了驗(yàn)證。
[Abstract]:With the rapid development of modern educational technology and artificial intelligence technology, the research on machine solution of subject question has become hot again. Compared with other disciplines, mathematics is a subject based on quantity and relationship. In this paper, the extraction and representation of solid information in plane geometry images are studied in order to help realize the machine solution of plane geometry problems. Aiming at the overlapping structure and dashed line of geometric entity detection, and according to the characteristics of plane geometry image, this paper tests the relevant algorithms of entity detection, and puts forward a variety of post-optimization processing strategies. A more robust entity detection process and high detection accuracy are realized. And then the useful information of geometric entities is extracted from the detection results. This information can be displayed directly as a result by uniform representation, which can help students understand and explore the solution of the problem independently, and can integrate with the text information. Get more complete information to help realize the machine solution of plane geometry problem. This paper mainly includes two parts. The first part consists of three steps: image preprocessing, geometric entity detection and detection optimization. Through experimental analysis and comparison, this paper selects adaptive Gao Si kernel binarization algorithm to binary plane geometry image, and marks the binary image with 8-connected domain. In order to segment the corresponding plane geometry and identification character areas. For the plane geometry region, the circular entity is first detected by RANSAC circle detection method, and the pixels of the circular entity are eliminated after the detection, and then the line segment entity is detected by the progressive probability Hough transform. Finally, through a large number of post-optimization processing to ensure a more robust detection effect, including connected domain label optimization, dashed line detection and recovery, all geometric entities based on the original coordinate system information is obtained. The second part is the extraction and representation of geometric entity information, which consists of three steps: OCR, entity information extraction and entity information representation. The OCR process of identifying character region is trained and recognized by BP neural network, and the corresponding result of identification character is integrated into the attribute information of the point entity nearest to the center of the current character region. At the same time, the effective entity information types in plane geometry image are summarized, and the corresponding extraction method based on coordinate system is given. Finally, according to the extracted entity information, the extended predicate representation, the equation system representation and the natural language representation are used for consistent representation. In this paper, a robust unified framework for extracting and representing geometric entity information is formed, and a large number of experiments are carried out on the collected image data sets, and the rationality and robustness of the framework are verified.
【學(xué)位授予單位】：華中師范大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：TP391.41;O182.1

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本文編號(hào)：2378507