Volume Based Mesh Segmentation
4.4 Experimental Results
the segmentation regions in Fig. 4.6.
4.4 Experimental Results
(a) hand (b) dinosaur (c) armadillo
(d) santa (e) nepture
Figure 4.8: The segmentation result of different models.
By using the volume information encoded in the MSP function, the proposed segmen-tation scheme can handle models of different topological types. Fig. 4.8 demonstrates the segmentation result for models shown in Fig. 3.2. Observed that the cut boundaries are located along the regions where there exists a large gap in MSP value and in the mean-time follow the object’s local features. Moreover, the salience-measure ensures that the most visually significant parts are segmented. The dinosaur (Fig. 4.8(b)) and armadillo (Fig. 4.8(c)) models have complex surface details and hence it is difficult to locate correct cut boundaries based on minima-rule alone. Since the MSP function is less sensitive to the
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surface detail noise, we can generate meaningful parts and reasonably good boundaries us-ing the proposed hybrid capacity on these two models. The nepture (Fig. 4.8(e)) model has genus higher than 1 and does not have obvious core-salient structure. Such kind of model can hardly be handled well using segmentation methods based on the global shape proper-ties such as averaged geodesic distance [36, 35]. On the other hand, the proposed method finds no difficulty on such models since the volume information encoded by MSP function is less global and provides enough cues for identifying the parts from the models. Some smooth artifacts on cut boundaries may still be observed on some segmentation results such as the cut boundaries between the hind legs and the body of the camel (Fig. 4.7) and be-tween the thighs and the body of the armadillo (Fig. 4.8(c)) and of nepture (Fig. 4.8(e)).
In such regions, the tip of the magnitude of MSP gradient has large amount of disturbance and twice of compensation term in Eq. 4.4 may be not enough for yielding smooth bound-aries. Moreover, we assume that the internal volume is uniform within the object part while noticeable volume change exists between parts. For models with some adjacent parts that have no noticeable volume change between them, our segmentation scheme may fail to separate them into different parts, such as the case in Fig. 4.8(e) where the hand and trident are not separated.
In Fig. 4.9, we compare the proposed method to other methods provided in the segmen-tation benchmark [10]. Cup and chair models do not have obvious core-salient structure on which the core extraction [35] and K-means [77] algorithms fail to produce good segmen-tations. The segmentation using SDF is based on a global fitting of the histogram function and is unable to reflect the local changes in object volume, leading to biased segmenta-tion boundaries. Moreover, the SDF cannot correctly describe the non-cylindrical part and generates improper segments on the cup model. The randomized cuts method [22] gener-ates good segmentation results for most of the models. However, its performance strongly depends on the segmentation methods based on local curvature and the geodesic distance.
In consequence, it may not generate good segmentations for models with complex local features. Fig. 4.10 shows the segmentation result of dinosaur model using the proposed scheme and the randomized cuts [22]. The proposed segmentation can tolerate the com-plex local features of the dinosaur model and segments the models into parts with similar salience significance. On the other hand, randomize cuts algorithm produces improper seg-mentation boundaries at the neck, the body, and the tail. We also perform the benchmark
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MSP Randomized Cuts SDF K-Means Core Extraction
Figure 4.9: Comparison of the segmentation methods.
(a) MSP (b) Randomized Cuts
Figure 4.10: Comparison of dinosaur result using MSP and randomized cuts [22].
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study of the proposed method against others using the segmentation benchmark [10]. The benchmark is obtained by performing the comparison based on 20 models selected from the object database of the segmentation benchmark (two models from each object category).
Fig. 4.11 reveals that the proposed segmentation scheme always yields lower error than the four other metrics proposed in [10].
(a) Cut Discrepancy (b) Hamming Distance
(c) RandIndex (d) Consistency Error
Figure 4.11: The benchmark of our segmentation method.
Since the interior volume of a model is almost constant during animation, the proposed segmentation scheme is inherently pose invariant. We list the segmentation result of the animated centaur model in four poses in the top of Fig. 4.12. The bottom of Fig. 4.12 illustrates the average error rate of MSP function for each of the four poses. For each pose, the MSP’s average error rate is computed by averaging the differences in MSP value between the pose and all other poses. The MSP is almost invariant to the change of pose, except in some joint regions where very small deviation of MSP value may exist.
We decompose the dinosaur and armadillo models into a hierarchy of four levels, as shown in Fig. 4.13. The columns from left to right indicate the levels in ascending order.
The most significant parts, such as the body of armadillo and the four limbs, are decom-posed at the first level. As going down in the hierarchy, we observe that parts at the same level have similar salience significance and parts in lower levels have less salience
signif-4.4 Experimental Results 38
0.012 0.009 0.011 0.015
Avg. error rate
pose 0 pose 1 pose 2 pose 3
Figure 4.12: Segmentation and average error rate for different poses of the animated centaur model.
icance. Fig. 4.14 depicts the histogram plots of salience-measure for the dinosaur model.
The parts having similar meaning tend to have similar values of salience-measure and will be decomposed at the same level. Fig. 4.15 lists the hierarchical segmentation result using SDF [73]. The boundaries of core part for the dinosaur and armadillo are varying among different levels. Parts at the same level might differ greatly in salience significance and, moreover, parts at lower levels may not have less salience significance.
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Figure 4.13: Hierarchical segmentation result of the dinosaur and armadillo models.
(a) Level 1 (b) Level 2 (c) Level 3 (d) Level 3
Figure 4.14: Histograms of the salience-measure at four levels for the dinosaur model.
Figure 4.15: Hierarchical segmentation result of the dinosaur and armadillo models using SDF [73].