附錄 附錄 附錄 附錄
1) 完整檢索數據
完整檢索數據完整檢索數據完整檢索數據在PSB資料庫中完整的檢索數據如表十一所示，在ESB資料庫中完整的檢索數 據如表十二所示，在SHREC-W資料庫中完整的檢索數據如表十三所示，在NIST資 料庫中完整的檢索數據如表十四所示。
表十一、在PSB資料庫中完整的檢索效能表，Recall (%)Re、DCG(%)和Query Time(s)。 Method 執行執行 執行執行
次數次數次數 次數
Re (NL=Ti)
Re (NL=2Ti)
Re (NL=3Ti)
Re (NL=4Ti)
DCG (kmax=907)
Query Time(s)
ART-ED[42] 42.32 52.29 58.15 62.13 71.83 0.1953
SGD[42] 26.39 34.10 40.06 44.41 58.65 0.0064
PPD[41] 34.04 43.92 49.89 54.43 65.62 0.0114
3D-ART[35] 35.89 45.11 49.78 53.10 66.68 0.0114
GD2[26] 28.66 38.03 43.72 48.21 61.34 0.0151
BD[25] 26.72 34.00 38.95 42.69 58.70 0.0163
FCBaseline 45.04 56.10 61.71 65.62 74.08 0.2353
FCBC 41.77 52.86 59.00 63.57 71.77 0.2871
FCIRP 43.12 55.43 61.95 66.23 73.72 0.2899
DMDFFRW 46.49 57.68 62.78 66.57 74.87 0.4256
DMDFAQPM
1 45.04 56.10 61.71 65.62 74.08 0.4690 2 47.69 59.14 64.63 68.22 75.71 0.4706 3 48.48 59.98 65.46 69.07 76.14 0.4723 4 48.96 60.13 65.85 69.34 76.29 0.4741 5 49.26 60.29 65.79 69.61 76.38 0.4751 6 49.21 60.34 65.90 69.74 76.40 0.4761 7 49.50 60.68 65.93 69.51 76.51 0.4764 8 49.19 60.48 65.80 69.58 76.36 0.4777 9 49.30 60.80 66.08 69.55 76.41 0.4795 10 49.34 60.61 65.91 69.65 76.28 0.4792
DMDFAQPM-FRW
1 46.49 57.68 62.78 66.57 74.87 0.4693 2 48.56 60.33 65.48 69.16 76.31 0.4708 3 49.23 60.98 66.46 69.99 76.62 0.4734 4 49.74 61.06 66.58 70.16 76.69 0.4749 5 49.94 60.99 66.49 70.51 76.83 0.4768 6 49.86 61.26 66.73 70.50 76.78 0.4765 7 50.01 61.37 66.77 70.54 76.88 0.4795 8 49.97 61.23 66.78 70.46 76.75 0.4802 9 50.05 61.48 66.96 70.30 76.70 0.4816 10 50.04 61.49 66.98 70.46 76.65 0.4818
表十二、在ESB資料庫中完整的檢索效能表，Recall (%)Re、DCG(%)和Query Time(s)。 Method 執行執行 執行執行
次數次數次數 次數
Re (NL=Ti)
Re (NL=2Ti)
Re (NL=3Ti)
Re (NL=4Ti)
DCG (kmax=907)
Query Time(s)
ART-ED[42] 41.55 54.90 63.01 68.15 76.23 0.1873
SGD[42] 31.95 42.49 49.55 55.65 69.80 0.0064
PPD[41] 36.43 46.84 54.22 59.72 72.98 0.0113
3D-ART[35] 41.30 54.82 61.35 65.98 75.86 0.0110
GD2[26] 35.36 45.97 52.50 57.32 71.87 0.0152
BD[25] 38.52 49.24 56.36 61.35 73.98 0.0162
FCBaseline 47.73 61.72 68.95 73.88 80.19 0.2254
FCBC 45.01 59.12 67.20 72.23 78.61 0.2730
FCIRP 45.96 59.96 67.88 73.30 79.26 0.2728
DMDFFRW 48.07 61.89 69.12 74.09 80.37 0.3866
DMDFAQPM
1 47.73 61.72 68.95 73.88 80.19 0.4227 2 48.64 62.53 69.89 74.53 80.54 0.4315 3 48.98 62.62 70.09 74.55 80.61 0.4341 4 49.03 62.97 70.34 74.92 80.66 0.4371 5 49.18 62.76 70.37 74.78 80.67 0.4380 6 49.15 63.04 70.56 75.00 80.58 0.4407 7 49.08 62.91 70.44 74.96 80.53 0.4416 8 49.03 63.05 70.45 74.97 80.52 0.4416 9 48.91 63.00 70.35 74.89 80.46 0.4424 10 48.80 63.06 70.41 75.09 80.42 0.4421
DMDFAQPM-FRW
1 48.07 61.89 69.12 74.09 80.37 0.4269 2 48.89 62.80 70.01 74.78 80.62 0.4349 3 49.30 62.76 70.30 74.76 80.71 0.4367 4 49.24 63.12 70.58 75.10 80.74 0.4407 5 49.49 63.01 70.59 74.90 80.72 0.4416 6 49.42 63.14 70.66 75.07 80.69 0.4442 7 49.30 62.97 70.67 75.09 80.61 0.4454 8 49.31 63.10 70.60 75.03 80.58 0.4458 9 49.27 63.25 70.46 75.09 80.52 0.4470 10 49.11 63.19 70.51 75.07 80.47 0.4478
表十三、在SHREC-W資料庫中完整的檢索效能表，Recall (%)Re、DCG(%)和Query Time(s)。
Method 執行執行 執行執行 次數 次數次數 次數
Re (NL=Ti)
Re (NL=2Ti)
Re (NL=3Ti)
Re (NL=4Ti)
DCG (kmax=907)
Query Time(s)
ART-ED[42] 46.64 59.40 68.33 74.55 80.37 0.0860
SGD[42] 36.03 52.06 61.24 67.78 72.46 0.0030
PPD[41] 42.05 56.24 65.84 71.94 77.67 0.0051
3D-ART[35] 43.38 55.24 62.09 67.17 78.00 0.0050
GD2[26] 42.21 56.87 65.81 71.80 77.13 0.0070
BD[25] 57.80 71.91 78.35 82.89 85.42 0.0071
FCBaseline 60.75 73.65 80.14 84.26 87.17 0.1036
FCBC 56.23 70.24 77.51 82.65 84.95 0.1146
FCIRP 56.91 72.30 79.05 83.84 85.92 0.1150
DMDFFRW 60.73 73.82 80.10 84.41 87.27 0.2237
DMDFAQPM
1 60.75 73.65 80.14 84.26 87.17 0.2597 2 63.68 76.06 81.46 85.39 88.53 0.2679 3 64.94 76.72 82.05 85.64 89.04 0.2655 4 65.38 77.20 82.32 85.84 89.18 0.2672 5 65.46 77.30 82.71 86.09 89.18 0.2689 6 66.11 77.36 82.80 86.19 89.23 0.2700 7 65.76 77.41 83.04 86.09 89.19 0.2711 8 65.94 77.67 82.77 86.23 89.18 0.2715 9 65.83 77.74 83.10 86.30 89.24 0.2727 10 65.94 77.90 82.90 86.26 89.21 0.2730
DMDFAQPM-FRW
1 60.73 73.82 80.10 84.41 87.27 0.2653 2 63.95 76.31 81.62 85.39 88.57 0.2669 3 65.11 76.82 82.06 85.75 89.06 0.2701 4 65.68 77.31 82.41 86.05 89.24 0.2720 5 65.64 77.49 82.75 86.16 89.23 0.2739 6 66.20 77.64 82.95 86.39 89.26 0.2748 7 66.03 77.65 83.02 86.14 89.26 0.2759 8 66.15 77.89 82.92 86.39 89.26 0.2765 9 66.03 78.06 83.17 86.36 89.30 0.2773 10 66.20 78.09 83.07 86.44 89.26 0.2775
表十四、在NIST資料庫中完整的檢索效能表，Recall (%)Re、DCG(%)和Query Time(s)。
Method 執行執行 執行執行 次數 次數次數 次數
Re (NL=Ti)
Re (NL=2Ti)
Re (NL=3Ti)
Re (NL=4Ti)
DCG (kmax=907)
Query Time(s)
ART-ED[42] 43.84 56.23 63.45 68.51 76.73 0.1721
SGD[42] 18.81 26.69 32.83 37.99 56.39 0.0056
PPD[41] 39.02 53.06 60.59 65.92 73.72 0.0096
3D-ART[35] 40.03 52.01 58.44 62.63 73.97 0.0097
GD2[26] 31.73 42.89 49.78 55.06 67.78 0.0138
BD[25] 23.79 31.24 36.42 40.75 60.51 0.0138
FCBaseline 48.20 60.59 67.09 71.95 79.68 0.2061
FCBC 45.09 58.79 66.67 71.88 77.44 0.2462
FCIRP 45.89 60.16 67.92 73.04 79.13 0.2434
DMDFFRW 49.96 62.48 69.14 73.83 80.78 0.3475
DMDFAQPM
1 48.20 60.59 67.09 71.95 79.68 0.3859 2 52.40 64.24 70.71 75.06 82.03 0.3849 3 53.83 65.71 72.01 75.88 82.79 0.3861 4 54.29 66.20 72.45 76.49 83.05 0.3861 5 54.60 66.61 72.80 76.77 83.19 0.3875 6 54.67 66.69 73.09 76.78 83.22 0.3881 7 54.74 66.82 73.14 77.10 83.25 0.3891 8 54.68 66.96 73.12 77.04 83.21 0.3898 9 54.76 66.91 73.19 77.17 83.21 0.3899 10 54.61 67.11 73.06 77.01 83.18 0.3906
DMDFAQPM-FRW
1 49.96 62.48 69.14 73.83 80.78 0.3869 2 54.08 65.95 72.39 76.43 82.88 0.3854 3 55.31 67.25 73.43 77.17 83.48 0.3864 4 55.71 67.76 73.74 77.69 83.70 0.3865 5 55.93 67.98 74.11 77.98 83.80 0.3884 6 56.09 67.85 74.19 78.02 83.75 0.3890 7 55.99 68.21 74.34 78.23 83.78 0.3894 8 55.97 68.27 74.28 78.10 83.74 0.3899 9 56.13 68.30 74.33 78.19 83.76 0.3907 10 55.88 68.35 74.28 78.18 83.75 0.3913
2) 加權特徵整合
加權特徵整合加權特徵整合加權特徵整合(Feature Re-weighting，，，，FRW)為了提高檢索的正確性，我們調整了各個特徵向量的權重值，計算各特徵距離的 加權總和，以此測量兩個3D模型的距離。在本論文，每個特徵的權重是利用先前所 選出相關模型和不相關模型的相關值來計算。
根據選出相關模型和不相關模型的相關值，第m個特徵的權重定義如下：
∑
∑
=
=
−
=
IRev Rev
1 1
) ( ) ( )
( ) (
N
j
j j
m N
i
i i m
m B r Rev r B ir Revir
ω (34)
Rev(ri)是第i個相關模型的相關值，Rev(irj)是第j個非相關模型的相關值，Bm(ri)和Bm(irj) 分別是判斷相關和非相關模型是否在Lm(在第m個特徵的檢索結果裡，排名前Q名的模 型)的布林函數，設定如下：
∈
= 0, otherwise ,
) 1
( m
m
L r r
B (35)
因此，如果Lm包含許多的相關模型，而且在檢索結果中名列前茅，那麼第m個特徵將 會取得很大的權重值，然後將使用加權距離來找出最相似的模型。
在PSB資料庫FRW(-)與動態多重特徵調整的檢索效能表如表十五所示，在ESB
資料庫 FRW(-)與動態多重特徵調整的檢索效能表如表十六所示，在 SHREC-W資料
庫FRW(-)與動態多重特徵調整的檢索效能表如表十七所示，在 NIST資料庫FRW(-)
與動態多重特徵調整的檢索效能表如表十八所示。
表十五、在PSB資料庫中FRW(-)與動態多重特徵調整的檢索效能表，Recall (%)Re、 DCG(%)和Query Time(s)。
Method 執行執行執行執行 次數次數 次數次數
Re (NL=Ti)
Re (NL=2Ti)
Re (NL=3Ti)
Re (NL=4Ti)
DCG (kmax=907)
Query Time(s)
DMDFFRW(-) 46.31 57.54 62.75 66.43 74.83 0.4745
DMDFAQPM-FRW(-)
1 46.31 57.54 62.75 66.43 74.83 0.5258 2 48.46 60.22 65.45 69.07 76.27 0.5306 3 49.03 60.92 66.45 69.91 76.57 0.5332 4 49.61 60.99 66.58 70.12 76.64 0.5355 5 49.93 61.01 66.41 70.42 76.81 0.5368 6 49.78 61.28 66.64 70.50 76.76 0.5379 7 49.92 61.34 66.65 70.49 76.82 0.5389 8 49.90 61.23 66.68 70.35 76.70 0.5401 9 50.09 61.44 66.82 70.35 76.68 0.5419 10 49.97 61.41 66.88 70.35 76.61 0.5421
表十六、在ESB資料庫中FRW(-)與動態多重特徵調整的檢索效能表，Recall (%)Re、 DCG(%)和Query Time(s)。
Method 執行執行 執行執行 次數次數次數 次數
Re (NL=Ti)
Re (NL=2Ti)
Re (NL=3Ti)
Re (NL=4Ti)
DCG (kmax=907)
Query Time(s)
DMDFFRW 48.15 61.89 69.06 74.14 80.37 0.4281
DMDFAQPM-FRW
1 48.15 61.89 69.06 74.14 80.37 0.4748 2 48.84 62.71 70.06 74.70 80.62 0.4822 3 49.25 62.75 70.27 74.74 80.71 0.4865 4 49.22 63.07 70.53 75.00 80.72 0.4897 5 49.43 63.04 70.61 74.87 80.71 0.4905 6 49.38 63.13 70.67 75.08 80.69 0.4939 7 49.25 63.03 70.70 75.05 80.61 0.4959 8 49.26 63.09 70.58 74.99 80.58 0.4979 9 49.25 63.19 70.48 75.04 80.51 0.4980 10 49.10 63.13 70.53 75.12 80.48 0.4987 表十七、在SHREC-W資料庫中FRW(-)與動態多重特徵調整的檢索效能表，Recall (%)Re、DCG(%)和Query Time(s)。
Method 執行執行 執行執行 次數次數次數 次數
Re (NL=Ti)
Re (NL=2Ti)
Re (NL=3Ti)
Re (NL=4Ti)
DCG (kmax=907)
Query Time(s)
DMDFFRW 60.66 73.80 80.09 84.40 87.24 0.2631
DMDFAQPM-FRW
1 60.66 73.80 80.09 84.40 87.24 0.2992 2 63.89 76.26 81.72 85.40 88.57 0.3039 3 65.11 76.80 82.10 85.73 89.05 0.3086 4 65.56 77.27 82.39 86.03 89.23 0.3111 5 65.59 77.46 82.70 86.16 89.22 0.3135 6 66.19 77.60 82.92 86.39 89.25 0.3150 7 65.94 77.59 83.01 86.17 89.24 0.3163 8 66.10 77.89 82.91 86.33 89.25 0.3168 9 66.08 78.02 83.09 86.35 89.29 0.3173 10 66.20 78.05 83.04 86.36 89.25 0.3186 表十八、在NIST資料庫中FRW(-)與動態多重特徵調整的檢索效能表，Recall (%)Re、 DCG(%)和Query Time(s)。
Method 執行執行 執行執行 次數 次數次數 次數
Re (NL=Ti)
Re (NL=2Ti)
Re (NL=3Ti)
Re (NL=4Ti)
DCG (kmax=907)
Query Time(s)
DMDFFRW 49.75 62.29 69.01 73.65 80.68 0.3913
DMDFAQPM-FRW
1 49.75 62.29 69.01 73.65 80.68 0.4316 2 53.90 65.84 72.28 76.36 82.83 0.4322 3 55.18 67.14 73.33 77.14 83.44 0.4339 4 55.59 67.69 73.68 77.68 83.67 0.4379 5 55.81 67.87 74.03 77.91 83.78 0.4363 6 55.93 67.81 74.14 77.99 83.75 0.4371 7 55.98 68.03 74.30 78.19 83.77 0.4378 8 55.88 68.18 74.24 78.08 83.72 0.4388 9 56.06 68.24 74.24 78.24 83.73 0.4399 10 55.79 68.26 74.28 78.16 83.74 0.4405
3) 錯誤率
錯誤率錯誤率錯誤率為了證明我們的自動相關不相關模型選擇機制是有效的，在本章節我們將計算其
錯誤率(Error Rate，ER)，而在這邊我們將計算兩種錯誤率，第一種是選擇相關模型的
錯誤率(ERiRev)，計算被選為相關模型卻與查詢模型不同類別的機率，可由以下公式 定義：
i i i
N ER NS
Rev Rev
Rev =1− (36)
NRevi 表示以第 i 個查詢模型自動選出的相關模型之數量，NSRevi 表示以第 i 個查詢模 型選出的相關模型中與查詢模型同類別的模型個數。第二種是選擇非相關模型的錯誤 率(ERIRevi )，計算被選為非相關模型卻與查詢模型相同類別的機率，可由以下公式定 義：
i i i
N ER NS
IRev IRev
IRev = (37)
NIRevi 表示以第i個查詢模型自動選出的非相關模型之數量，NSiIRev表示以第i個查詢 模型選出的非相關模型中與查詢模型同類別的模型個數。整體平均的相關模型錯誤率 (ERRev)和非相關模型錯誤率(ERIRev)定義如下：
∑
∑
=
=
×
= s s
N
i i N
i
i i
N ER N
ER
1 Rev 1
Rev Rev
Rev (38)
以及
∑
∑
=
=
×
= s
s
N
i i N
i
i i
N ER N
ER
1 IRev 1
IRev IRev
IRev (39)
如表十九所示，我們將計算出四個資料庫中平均的相關與非相關模型錯誤率。
表十九、在四個資料庫中，相關與非相關模型的平均錯誤率。
資料庫 資料庫 資料庫
資料庫 ERRev (%) ERIRev(%)
PSB 26.80 3.56
ESB 15.46 9.29
SHREC-W 8.36 5.49
NIST 14.68 4.19
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