流場設計被廣泛的運用在電腦圖學與視覺化的呈現上，但在現今用來設計流場的方法裡，多為讓使用者去放置奇異點，進而控制流場的拓樸結構，但此方法也會讓流場中奇異點的位置與個數是難以預測的，而也不易管理流場的結構。在此論文中，最後所產生的流場將要依照原始影像上的流向變化來作設計，並且在遵循影像中的流向變化下，保持流場中的奇異點數量最少。演算法一開始將以圖片上已存在的梯度變化來產生流向，利用流向與顏色來進行superpixel 的分群，在分群結果的流向場上以superpixel為基準讓使用者去尋找出流向場上的奇異點，經由那些奇異點，去trace 出separatrix(分割線)，利用separatrix 找出每一個分割區域後，經由growing可以將所有的superpixel 指定給現有的切割範圍內，最後smooth邊界，產生邊界平滑的分割區域。

在流場設計部分，自動化設定流場型態，並利用骨架產生標準流場，透過Candidate list裡的組合去計算誤差值，保留誤差值最小的組合作為設定流場流入與流出的位置，最後在判別是否要將奇異點位置合併，以減少奇異點個數。

在產生完流場後，將整體流場渲染成類似油畫風格的結果。

Line field design is widely used in computer graphics and computer vision. But most of these method designed line field are letting user to put some singularities and to control the topology of whole flow field. However, it is extremely complexity to forecast the amount of singularities and their location, and even hard to administer the topology.

In our research, we will present a semi-automatic system. Our system will generate flow field which is following the gradient flow in original image, after that we will keep the fewest number of singularities. The input image separates into patches based on the existed gradient flow and color. Then, generating flow field with superpixel, and letting user find out singularities. It could trace separatrices bi-directly from these singularities as start point. We will get closed regions from separatrice, and assign undefined superpixels into existed patches. Finally, using voting scheme and get smooth edge.

In flow field design, we set flow type automatically, and generate standard flow field with skeleton structure. Then, it will be settled down the source/sink with the minimal error calculating between all line fields of combinations and standard flow field. Ultimately, we will check to merge singulaities, and try to keep the fewest number of singularities.

After the system generated the line field, it will represent the line field by rendering as painterly stylization. Our system would imitate the style of painterly by rendering stroke texture.

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