Segmentation transfer

When the models have large structural differences, the mothod of elector voting may gen-erate wrong correspondences such as in figure 6.9(a). It is a partial correspondence problem which attempts to find the human shape from the centaur models. Compare with the figure 6.9(a), our method produces more semantically correct result as shown in figure 6.9(b).

(a) Results of elector voting. (b) Our results.

Figure 6.9: The comparison with [ATCO⁺10] on Human and Centaur models.

6.2 Segmentation transfer

Figure 6.10, 6.11 and 6.12 show our segmentation transfer results for a variety of models in-cluding four-legged animals, human, and dragons. The source models in figure 6.10(a), 6.11(a) and 6.12(a) are framed by a red box. All the target models have consistent segmentations with source models such that the corresponding segment pairs are colored in the same colors. Figure 6.10 and 6.10 show the different types of segmentation for the four-legged animals. For the legs of the source animal in figure 6.10(a), the boundaries cross the legs vertically and form the short, straight shapes. In figure 6.11(b), the boundaries cross the legs in the tilted manners and form the more longer shapes. We can see that all the target models reproduce these characteris-tics since the fitting planes of the boundaries are transferred from the source models to the target models (section 5.4). Especially notice the differences between the horse in figure 6.10(b) and

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6.11(c), the wolf in figure 6.10(c) and 6.11(d), the deer in figure 6.10(g) and 6.11(b). Once the skeleton correspondences have been established, the segmentation transfer can be performed to the models with large shape and geometry differences, as shown in figure 6.12. According to the skeleton correspondences, the target model may not have some parts compared to the source model. For example, the dragon in figure 6.12(e) does not have the ears, and the human in figure 6.12(c) does not have the tail and ears. In such case the boundaries of these parts of the source model will not be transferred to the target model.

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(a) Goat. (b) Horse. (c) Wolf.

(d) Reindeer. (e) Camel. (f) Giraffe.

(g) Deer. (h) Pig.

Figure 6.10: Segmentation transfer results (sec. 1).

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(a) Pig. (b) Deer.

(c) Horse. (d) Wolf. (e) Goat.

Figure 6.11: Segmentation transfer results (sec. 2).

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(a) Dog. (b) Deer. (c) Human.

(d) Armadillo. (e) Dragon. (f) Triceratops.

(g) Elephant. (h) Asian dragon.

Figure 6.12: Segmentation transfer results (sec. 3).

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We also demonstrate the segmentation transfer results for the other categories of models in the Princeton Segmentation Benchmark dataset. Note that the figure 6.16 illustrates a limitation of our method. When the models have different topological shapes, our method may produce inconsistent results. The seat and back of the chair in figure 6.16(c) can not be separated since there is no boundary on some pillars.

(a) Source. (b) Target. (c) Source. (d) Target.

Figure 6.13: Segmentation transfer results of Ant and Teddy models.

(a) Source. (b) Target. (c) Source. (d) Target.

Figure 6.14: Segmentation transfer results of Bird and Fish models.

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(a) Source. (b) Target 1. (c) Target 2.

Figure 6.15: Segmentation transfer results results of Armadillo models.

(a) Source. (b) Target 1. (c) Target 2.

Figure 6.16: Segmentation transfer results of Chair models.

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We first compare our apporach with the method proposed by Golovinskiy and Funkhouser [GF09]. Figure 6.17 shows the comparison. For the models which have large differences in shapes or poses, the rigid alignment used in [GF09] is Insufficient to correctly build the face correspondences between the models, and then disturbs the segmentation results. Our method achieves better results since the skeleton matching is more robust to construct the part-based correspondences between the models which have large differences.

(a) Results of [GF09]. (b) Our results.

Figure 6.17: The comparison with [GF09] on Giraffe and Horse models

We also compare our apporach with the method proposed Kalogerakis et al. [KHS10] which simultaneously produces consistent segmentation and labeling on a set of models. Our method is more capable of controlling the number and location of the boundaries since our method is boundary based. We map the boundaries to the correspondence parts, and the segments are deduced from them. Compare the differences to rightmost airplanes in figure 6.18 and the gi-raffes in figure 6.19. However, for the models which have different shapes, some additional part will have no boundary and may cause inconsistent results, as shown in figure 6.20. Besides, our method only requires one source model, merely takes few seconds to complete segmenta-tion transfer to a target model (see secsegmenta-tion 6.3). In contrast, [KHS10] needs multiple models which have attached labels, and costs several hours for training. But due to the constraint of the

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skeleton construction, our method is suitable to produce part-type segmentation on the articu-lated models, and is restricted on some man-mode models such as the cup, table and mech of the Segmentation Benchmark [CGF09]. On the other hand, [KHS10] can well handle all cate-gories of the models of the Segmentation Benchmark with any type of segmentation including part-type and patch-type.

(a) Results of [KHS10].

(b) Our results.

Figure 6.18: The comparison with [KHS10] on Airplane models

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(a) Results of [KHS10].

(b) Our results.

Figure 6.19: The comparison with [KHS10] on Four-legged Animals models

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(a) Results of [KHS10]. (b) Our results.

Figure 6.20: The comparison with [KHS10] on Chair models

We employ the evaluation metrics proposed in [CGF09] to compare our method with other seven recent automatic segmentation algorithms. Where cut discrepancy measures the position deviation of the boundaries, and hamming distance, randindex, consistency error measure the dissimilarity of the segments. We use ground truth results provided in Segmentation Bench-mark [CGF09] as our input source segmentations and apply our method to the same category of models. The categories of the testing models include human, ant, chair, teddy, bird, fish, armadillo and four-legged animals. To have a fair comparison, for each automatic segmentation algorithm we manually reserve the results which are most similar to our input source segmen-tations (consider the number of segments and the similarity of the segmentation style), then run the benchmark evaluation. Since our method performs the parameterization and snake refine-ment, the boundary of our results may not lie on the edges of the original mesh. To satisfy the input of the benchmark evaluation, we clamp each point of the boundary to the closest vertex of the original mesh. Figure 6.21 shows the evaluation results. Our segmentation results are closest to ground truth. It implies that if a user provides with a good segmentation reference, our algorithm could generate higher quality results than other algorithms do.

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(a) Cut Discrepancy. (b) Hamming Distance.

(c) RandIndex. (d) Consistency Error.

Figure 6.21: Comparison with other segmentation algorithms using four evaluation metrics.