本研究的內容是一個以多邊形 (PLY) 檔案格式呈現的三維點雲，其中每個點由一組不規則的三維座標和 RGB 全彩屬性組成。在對點雲進行壓縮之前，每個點的 RGB 全彩屬性首先轉換為 YUV 屬性。本文提出了一種基於 Hilbert 曲線掃描順序的排序方法，以遞增的 Hilbert 曲線掃描順序重新排序點雲的不規則 3D 座標和相關的色彩屬性，使得重新排序後的鄰近點之間的空間距離可以減小。接下來，基於抽樣率 $\frac{1}{k}$，將排序後的 Hilbert 曲線掃描順序的點分成 $\lceil\frac{n}{k}\rceil$ 個區塊，其中 $n$ 表示點雲的點數。進一步計算每個區塊中 $k$ 個點的質心，並以區塊中最接近質心的點作為該區塊的抽樣點。最後，將排序後的 Hilbert 曲線掃描順序的座標和抽樣後的 YUV 屬性構成的抽樣點雲送入幾何點雲壓縮 (G-PCC) 標準的編碼器進行點雲屬性壓縮編碼。編碼後的位元流傳入解壓器解碼，本文提出了一種同時考慮距離與亮度的聯合雙邊插值方法重建抽樣點雲。基於典型的點雲數據和在 G-PCC 下進行了全面的實驗，與區域適應性分層轉換 (RAHT) 編碼器和最先進的方法相比，我們的方法在客觀質量、知覺效果和品質位元率權衡方面的優勢已得到充分證明。

Given a 3D point cloud in polygon (PLY) file format, in which each point consists of an irregular 3D position and the RGB full-color attribute. Prior to compressing the point cloud, the RGB full-color attribute of each point is first transformed into a YUV attribute. In this thesis, a sorted Hilbert curve scan order-based method is proposed to reorder the irregular 3D positions and the associated color attributes of the point cloud in an increasing Hilbert curve scan order such that the spatial distance between two neighboring reordered points can be reduced. Next, based on the downsampling rate, namely $\frac{1}{k}$, the sorted Hilbert curve scan order-based points are partitioned into $\lceil\frac{n}{k}\rceil$ blocks where $n$ denoted the number of points in the point cloud. Further more, the centroid of the $k$ points in each partitioned block is calculated, and taking the centroid as a base, the nearest neighboring point in the block is determined as the downsampled point. Finally, the downsampled point cloud, which consists of the sorted Hilbert curve scan order-based positions and the downsampled YUV attributes, is fed into the encoder of the Geometry-based Point Cloud Compression (G-PCC) standard for point cloud attribute compression. The encoded bitstream is fed into the decoder. In this thesis, a joint bilateral interpolation method that considers distance and luminance is proposed to reconstruct the downsampled point cloud. Based on typical testing point clouds and under G-PCC, comprehensive experimental data have justified the objective quality, perceptual effect, and quality-bitrate tradeoff merits of the proposed method when compared with the region adaptive hierarchical transform (RAHT) encoder and a state-of-the-art method.

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