Appendix A Additional results A.1 Benchmarks
A detailed qualitative and quantitative comparison of state-of-the-art MVS methods on all scans in
Tanks and Temples ( T&T ) dataset, as shown in Table 7, Table 8 and Fig.7.
ElasticMVS achieves state-of-the-art performance among all supervised and self-supervised MVS methods and the tremendous performance improvement in T&T advanced benchmark, demonstrating the effectiveness and robustness of the proposed ElasticMVS to complex categories and geometries.
The qualitative comparisons of all scenes in the T&T dataset also demonstrate that ElasticMVS precisely reconstructs the scenes with higher completeness and less noise.
[Table]
[Table]
[-× W × 3in the scene space given the camera matrix M : e = { e p ∗ ∈ R 
-]
[Table]
[Table]
B Elastic part representation[-is trainedwith a Feature Pyramid Network , whichshares the same structure as in PatchmatchNet (Wang et al., 2021a). To train thenetwork, we use the SGD (Bottou, 2010)with an initial learning rate of 1 . 
 × 10 − 4 . The threshold ϵ for defining S p is set to0 .-]
B.
1 Training loss
Visualizations of the elastic part representation representation compared with variants trained without confidence map (w/o Con.) and spatial concentration loss (w/o Spa.), which are shown in Fig 8 and
Fig 9.
Our elastic part representation successfully recognizes the part on the same physical surface with elastically-varying scales, shapes and boundaries.
B.2 Representation Comparison
We compare our elastic part representation with part representations in SLIC [2] and JDACS [43].
Since SLIC and JDACS both represent parts using labels that are different from our embedding-based representation, we highlight those pixels sharing the same label with the reference pixel denoted by the black "+".
As shown in Fig 10, Our elastic part representations are more scalable in size while also better preserving object boundaries.
C ElasticMVS C.1 Propagation
To better understand the effect of part-aware propagation we visualize the sampled candidates for propagation (blue points) during 3 iterations of patchmatch given six pixels (red points), which are shown in Fig 11.
As expected, the receptive field for hypotheses propagation is elastically changed according to the the geometric shape and the texture pattern of the object.
C. Number of iterations
The quantitative results with different number of hypothesis ( K p , K r ) under each iteration described in Sec.
3.2 are summarized in Fig.
Obviously, the error converges after only 4 iterations of patchmatch using different number of hypotheses.
Besides, using more hypotheses leads to faster convergence.
Apart from that, our part-aware patchmatch is robust to the diverse initialization and local perturbation.
C.3 Confidence map
The depth map predicted in each iteration is not always reliable, especially in textureless and highreflectant areas.
Therefore, we integrate multi-view geometric consistency constraints into the photometric consistency to increase the reliability and the accuracy of training and propagation.
The visualization of each part is demonstrated in Fig.
We diminish reconstruction artifacts by firstly using a bilaterally weighted adaption of normalized cross correlation to measure the photometric consistency c pho p between a reference view with the corresponding source views.
After that, the geometric consistency c geo p is computed as the forward-backward reprojection error between multiple views [34]. Besides, we compute surface smoothness c smo p [35] to find smooth surface parts, which is the angle between surface normals of adjacent image points.
This term identifies sudden changes of the surface normal direction at object edges [37], which is robust w.r.t.
noisy normal vectors. As shown in Fig. 13, for each reference image, the photometric consistency c pho p (b), geometric consistency c geo p (c) and surface smoothness c smo p (d) for each pixel p is separated computed. The final confidence c p (e) for training and propagation is the combination of these three factors: c p = c pho p
[Equation] p [Equation]