An Improved Surface Simplification Method for Facial Expression Animation Based on Homogeneous Coordinate Transformation Matrix and Maximum Shape Operator

Table 1

RMS error comparison between our method and DSD (unit: 10⁻²).

Triangles	The DSD	Our method	Improvement rate
Face 01 (fury)
5000	5.7313	0.8427	85.30%
2000	11.3899	1.6240	85.74%
1000	22.9495	2.6013	88.67%
500	42.7859	4.7140	88.98%
Face 02 (surprise)
5000	4.8805	1.4011	71.29%
2000	9.6882	2.7791	71.31%
1000	21.3109	4.2362	80.12%
500	37.8799	6.6230	82.52%
Face 03 (anger)
5000	4.6126	1.1371	75.35%
2000	9.1516	2.3843	73.95%
1000	19.3625	3.9031	79.84%
500	35.8760	6.6498	81.46%
Face 04 (grin)
5000	5.2081	1.3187	74.68%
2000	10.2029	2.4012	76.47%
1000	21.2078	3.8791	81.71%
500	39.2217	6.6697	82.99%
Face 05 (laugh)
5000	4.8700	1.2308	74.73%
2000	10.1936	2.4448	76.02%
1000	21.3471	3.8759	81.84%
500	39.3825	6.5277	83.42%
Face 06 (rage)
5000	5.3178	1.1113	79.10%
2000	10.2902	2.3494	77.17%
1000	21.0917	3.6617	82.64%
500	37.7458	5.6601	85.00%
Face 07 (sad)
5000	4.6088	1.4588	68.35%
2000	9.9824	2.9477	70.47%
1000	21.0213	4.4211	78.97%
500	38.0176	7.1686	81.14%
Face 08 (smile)
5000	4.6887	1.1734	74.97%
2000	9.8362	2.4347	75.25%
1000	21.4011	3.7970	82.26%
500	39.8993	5.9372	85.12%