Sketching as a universal form of communication provides arguably the most natural and direct way for humans to render and interpret the visual world. While it is not challenging for human viewers to interpret missing 3D information from single-view sketches, multi-view inputs are often needed for computer algorithms to recover the underlying 3D geometry due to the inherent ambiguity in single-view sketches. A key problem for interpreting multi-view sketches of the same object is to establish semantic correspondence among them. This problem has been mainly studied for 3D geometry reconstruction from careful engineering drawings in orthographic views . The problem of establishing semantic correspondence from rough sketches in arbitrary views (e.g., those in Figure 1 (Bottom)) is challenging due to shape abstraction and distortions in both shape and view, and is largely unexplored. Addressing this problem can benefit various applications, e.g., designing a novel interface for users with little training in drawing to create 3D shapes using multi-view sketches.
In this work we take a very first step to learn to establish semantic correspondence between freehand sketches depicting the same object from different views. This demands a proper shape descriptor. However, traditional descriptors like Shape Context  and recent learning-based patch descriptors [47, 34, 48] are often designed to be invariant to 2D transformation (rotation, translation, and limited distortion) and cannot handle large view changes (e.g., with view disparity greater than 30 degrees.) Such descriptors, especially used for the applications of stereo matching [19, 49, 7, 32, 55] and image-based 3D modeling [50, 29], heavily exploit the features containing textures and shadings of images for inferring similarities among different points or image patches, and thus are not directly applicable to our problem. This is because sketches only contain binary lines and points, exhibiting inherent sparsity and ambiguity.
We observe that human viewers can easily identify corresponding points from sketches with very different views. This is largely because human viewers have the knowledge of sketched objects in different views. Our key idea is thus to adapt deep neural networks previously used for learning patch-based descriptors but get the networks exposed to corresponding patches from multi-view sketches.
Training deep neural networks requires a large-scale dataset of sketch images with ground truth semantic correspondence. Unfortunately such training datasets are not available. On the other hand, manually collecting multi-view hand-drawn sketches and labeling the ground-truth correspondence would be a demanding task. Following previous deep learning solutions for 3D interpretation of sketches [37, 12, 26], we synthesize the multi-view line drawings from 3D shapes (e.g., from ShapeNet ) by using non-photorealistic rendering. Given the synthesized dataset of multi-view line drawings as sketches, we project the 3D vertices of 3D models to multi-view sketches to get ground-truth correspondences (Figure 2). This data generation pipeline is to emphasize the correspondence from 3D shapes and force deep networks to learn the valuable 3D correspondences among 2D multi-view sketches.
We formulate the correspondence learning problem into a metric function learning procedure and build upon the latest techniques for metric learning and descriptor learning . To find an effective feature descriptor for multi-view sketches, we combine a patch-based representation and a multi-scale strategy (Figure 3) to address the abstraction problem of sketches (akin to Sketch-A-Net ). We further design a multi-branch network (Figure 4) with shared-weights to consume the patches in different scales. The patch-based representation helps the network specify the local features of a point on a sketch image by embedding the information of its neighboring pixels. Our multi-scale strategy feeds the network with the local and global perspectives to learn the distinctive information in different scales.
The multi-scale patch representation allows the use of ground-truth correspondences that are away from sketch lines as the additional training data. This not only improves the correspondence accuracy but also enables correspondences inside the regions of sketched objects (e.g., the cup in Figure 1), potentially benefiting applications like sketch-based 3D shape synthesis. We evaluate our method by performing multi-view sketch correspondence pixel-wise retrieval tasks on a large-scale dataset of synthesized multi-view sketches based on three shape repositories: ShapeNet, Princeton Segmentation Benchmark (PSB)  and Structure Recovery  to show the effectiveness of our proposed framework. We also test our trained network on hand-drawn sketches (Figure 1) and show its robustness against shape and view distortions.
Our contributions are summarized as follows:
To the best of our knowledge, we are among the first to study the problem of multi-view sketch correspondence.
We introduce a multi-branch network to learn a patch-based descriptor that can be used to measure semantic similarity between patches from multi-view sketches.
We present a large-scale dataset consists of 6,852 multi-view sketches with ground-truth correspondences for 18 categories, and will release the dataset to the research community.
2 Related Work
We review the literature that is closely related to our work, namely, the approaches for correspondence establishment in images, and the approaches for sketch analysis using deep learning technologies.
2.1 Correspondence Establishment in Image Domain
Image-based Modeling and Stereo Matching.
Image-based modeling often takes as input multiple images of an object [29, 1] or scene [50, 45] from different views, and aims to reconstruct the underlying 3D geometry. A typical approach to this problem is to first detect a sparse set of key points, then adopt a feature descriptor (e.g., SIFT ) to describe the patches centered at the key points, and finally conduct feature matching to build the correspondence among multi-view images. Stereo matching [19, 49] takes two images from different but often close viewpoints, and aims to establish dense pixel-level correspondence across images. Our problem is different from these tasks in the following ways. First, the view disparity in our input sketches is often much larger. Second, unlike natural photos, which have rich textures, our sketches have more limited information due to their line-based representation.
Local Image Descriptors.
Local image descriptors are typically derived from image patches centered at points of interest and designed to be invariant to certain factors, such as rotation, scale, or intensity, for robustness. Existing local image descriptors can be broadly categorized as hand-crafted descriptors and learning-based descriptors. A full review is beyond the scope of this work. We refer the interested readers to  for an insightful survey.
. The conventional local descriptors are mostly built upon low-level image properties and constructed using hand-crafted rules. Recently, learning-based local descriptors produced by deep convolutional neural networks (CNNs)[47, 34, 48] have shown their superior performance over the hand-crafted descriptors, owing importantly to the availability of large-scale image correspondence datasets [52, 2] obtained from 3D reconstructions. To learn robust 2D local descriptors, extensive research has been dedicated to the development of CNN designs [18, 58, 47, 59, 51]23, 38, 3, 34, 21, 35] and training strategies [44, 8, 33]. The above methods, however, are not specially designed for learning multi-view sketch correspondence. The work of GeoDesec  shares the closest spirit with ours and employs geometry constraints from 3D reconstruction by Structure-from-Motion (SfM) to refine the training data. However, SfM heavily depends on the textures and shadings in the image domain, and is not suitable for sketches.
Multi-scale Strategy for Descriptors
Shilane and Funkhouser  computed a 128-D descriptor at four scales in spherical regions to describe distinctive regions on 3D shape surfaces. Recently, Huang et al.  proposed to learn 3D point descriptors from multi-view projections with progressively zoomed out viewpoints. Inspired by these methods, we design a multi-scale strategy to gather local and global context to locate corresponding points in sketches across views (Figure 3). Different from , which focuses on rendered patches of 3D shapes, our work considers patches of sparse line drawings with limited textures as input. To reduce the network size and computation, we adopt a smaller input scale  rather than in . In addition, Huang et al.  used three viewpoints for 3D point descriptors, while our work learns descriptors of points in sketches drawn under a specific viewpoint for correspondence establishment across a larger range of views.
2.2 Deep Learning in Sketch Analysis
With the recent advances in deep learning techniques, a variety of deep learning based methods have been proposed for sketch analysis tasks such as fine-grained sketch-based image retrieval, sketch synthesis , sketch segmentation , sketch retrieval , and sketch recognition . However, none of these existing solutions can be directly applied to our task. To make deep learning possible in sketch analysis, there exist multiple large-scale datasets of sketches including the TU-Berlin , QuickDraw , and Sketchy  datasets. However, they do not contain multi-view sketches and thus cannot be used to train our network. A sketch is generally represented as either a rasterized binary-pixel image 
or vector sequences[17, 28] or both . Since it is difficult to render line drawings from 3D shapes as a sequence of well-defined strokes, we use rasterized binary-pixel images to represent our training data and input sketches.
Multi-view Sketch Analysis
Multi-view sketches are often used in sketch-based 3D modeling [39, 37, 31, 12, 26]. Early sketch-based modeling methods (e.g., ) require precise engineering drawings as input or are limited by their demanding mental efforts, requiring users to first decompose a desired 3D shape into parts and then constructing each part through careful engineering drawings . To alleviate this issue, several recent methods [37, 31, 12, 26] leverage learning-based frameworks (e.g., GAN ) to obtain the priors from training data and then infer 3D shapes from novel input multi-view sketches (usually in orthographic views, namely, the front, back, and side views). However, these methods often process individual multi-view sketches in separate branches and do not explicitly consider semantic correspondence between input sketches.
SketchZooms by Navarro et al.  is a concurrent work and studies the sketch correspondence problem with a similar deep learning based solution. Our work is different from SketchZooms as follows. To generate the training data for cross-object correspondence, the used 3D shapes need to be semantically registered together in advance in SketchZooms, while our work explores training data generation from individual 3D shapes for cross-view correspondence. SketchZooms follows [20, 46] and adapts AlexNet  (40M parameters) with the final layer replaced with a view pooling layer. In contrast, our designed framework has a smaller size (1.4M parameters), and its high performance and efficiency shown in our experiments pave a path for our method to be more easily integrated into mobile/touch devices.
Terminology. To standardize different expressions for points in the following sections, we refer to the points on the surface of a 3D shape as vertices; the points on a 2D sketch image as pixels; and the points exactly on the sketch lines as points.
For input sketches represented as rasterized images, a key problem to semantic correspondence learning is to measure the difference between a pair of pixels in a semantic way. This is essentially a metric function learning problem where a pair of corresponding pixels get a shorter distance than a pair of non-corresponding pixels in the metric space. Formally, it can be expressed as follows:
where is a metric function, and and represent corresponding pixels from different sketches (e.g., a pair of positive and anchor in Figure 3) while and are a pair of non-corresponding pixels (e.g., a pair of anchor and negative).
We follow  to build the metric function by learning a sketch descriptor (SketchDesc) with a triplet loss function. Since sketch images are rather sparse, we adopt a multi-scale patch-based representation, with a multi-scale patch centered at a pixel of interest in a sketch. We resort to deep CNNs, which own the superior capability of learning discriminative feature descriptors from sufficient training data. As illustrated in Figure 4, our designed network (Section 3.2) takes a multi-scale patch as input and outputs a 128-D semantically meaningful distinctive descriptor.
To train the network, we first synthesize line drawings of a 3D shape from different viewpoints as multi-view sketches. We then generate the ground-truth correspondences by first uniformly sampling points on the 3D shape and then projecting them to the corresponding multiple views. We will discuss the detailed process of data preparation in the following section.
3.1 Data Preparation
Multi-view Sketches with Ground-truth Correspondences.
We follow a similar strategy in [27, 53, 46] to synthesize sketches from 3D shapes. Specifically, we first render a 3D shape with aligned upright orientation to a normal map under a specific viewpoint, and then extract an edge map from the normal map using Canny edge detection. We adopt this approach instead of the commonly used suggestive contours , since the latter is designed for high-quality 3D meshes and cannot generate satisfactory contours from poorly-triangulated meshes (e.g., airplanes and rifles in the Structure Recovery dataset ). Hidden lines of the edge detection results are removed. In our implementation, each sketch is resized to a image. As mentioned in , since most humans are not faithful artists and they create sketches in a casual and random way, only three clustered views  or limited canonical views  may not be enough to cover the situations how people express the correspondence. To obtain more general multi-view sketches, we uniformly sample 12 viewpoints on the upper unit viewing hemisphere (in the elevation angle of 1545 degrees for each 3D model.
By projecting each vertex to the corresponding views, we naturally construct ground-truth correspondences (with the projections from the same vertices) among synthesized multi-view sketches, as illustrated in Figure 2. We do not consider hidden vertex projections (invisible under the depth test). If the projections of a vertex are visible only in less than 2 different views, this vertex is not considered in ground-truth correspondences.
Multi-scale Patch Representation.
We represent each visible projection of a 3D vertex on sketch images with a patch-based representation centered at the corresponding pixel to capture the distinctive neighboring structures (Figure 3). To further handle the issues due to the sparsity of sketches and the lack of texture information, we adopt a multi-scale strategy. Given a sketch image, we employ a four-scale representation (i.e., , , , and ) for a pixel, as illustrated in Figure 3.
The multi-scale patch-based representation allows us to sample ground-truth correspondences inside sketched objects, not necessarily on sketch lines. This significantly increases the number of ground-truth correspondences. However, we do require non-zero information in a multi-scale patch. We have tried two sampling mechanisms: 1) OR-sampling: a multi-scale patch is valid if the patch is non-empty at any of the scales (Figure 5 (Left)); 2) AND-sampling: a multi-scale is valid if the patch is non-empty at every scale (Figure 5 (Left)). The former often makes a multi-scale patch at almost every visible vertex projection valid, since the patch at scale is often non-empty given its relatively large scale. Instead, the AND-sampling leads to the use of patches near to the sketch lines only. We will compare the performance of these two sampling mechanisms in Section 4.
3.2 Network Architecture
We design a network architecture to learn a descriptor for measuring semantic distance between a pair of points in multi-view sketches. As illustrated in Figure 4, our network has four branches to process the four-scale input patches. The four branches share the same architecture and weights in the whole learning process. Each branch receives a 32 32 patch and outputs a 128 1 (i.e., 128-D) feature vector which is then further fused at the concatenation layer and the final full-connected layer. Note that due to the shared weights among the branches, the multi-branch structure does not increase the number of parameters. Our network produces a 128-D descriptor as output, which will be later used for sketch correspondence and pixel-wise retrieval in Section 4.
3.2.1 Design Choices
To accommodate the sparse nature of the sketch patches, in the initial design stage we experimented with several network schemes for sketches. They seem common in the image domain, i.e., attention and short-cut connection in ResNet, but we did not observe any significant improvement over our current network architecture. Below we briefly discuss our attempts and hope they are inspiring for the readers to explore alternative solutions.
As reported in , the active regions in sparse inputs like line drawings become blurrier due to their diffusion to empty regions. after passing through several convolution layers. To obtain the features tightly along the edges in sketch patches, one option is to utilize the input sketch patch itself as a mask to filter the diffused regions in the feature maps after every convolution layer. However, we find that this operation will reduce the number of active regions in the feature maps, leading to degenerated results.
A possible way to address the limited context in sparse input sketches is to gather more information from previous layers to the current layer. However, this strategy achieves a comparable performance to our current network framework.
3.3 Objective Function
To train our network, we organize the training data as triplets of patches (Figure 3) and feed them to our network. We define the output features of a triplet as (), where is the feature vector of an anchor pixel in one sketch, and and represent the features of the corresponding pixel (corresponding to the same vertex in a 3D shape as the anchor pixel) and a non-corresponding pixel. The non-corresponding pixel can be selected from either the same sketch or in the other views. With the feature triplets, we adopt the triplet loss  to train the network. The triplet loss given in Equation 2 aims to pull the distance between feature descriptors of a pair of corresponding points () and push away the distance between a pair of non-corresponding points () in the metric space.
where is the number of triplets in a training batch, denotes the -th triplet, measures the Euclidean distance given two features, and the margin is set as in our experiments.
We conduct extensive experiments on a multi-view sketch dataset synthesized from three existing 3D shape repositories: the Structure-Recovery database , Princeton Segmentation Benchmark (PSB)  and ShapeNet . Table 1 shows the detailed information of the number of 3D shapes, the names of selected categories, as well as the number of views used in each dataset.
We also evaluated on a dataset of hand-drawn sketches. Our current evaluation focused on the chair category, since chairs have rather complicated geometry and structure. Several participants were invited to create test sketches. They were asked to create sketches on a touchscreen by recollection, after observing the model for a fixed amount of time. Each participant was given 3 salient views that ordinary users are familiar of, to sketch for. Figure 1 (Bottom) shows some representative results of sketch correspondence.
4.1 Implementation Details
We train our network category-wise for a specific object category with a data splitting ratio of 8 : 1 : 1 (training : validating : testing). All multi-view sketches are rendered to the size of . The batch size is set as . We sample the training triplets in a batch randomly. Our network is trained on the Graphics Card RTX
Ti and optimized by the Adam optimizer. The learning rate and number of iteration epochs in our experiments are set toand , respectively.
4.2 Performance Evaluation
To verify the effectiveness of our proposed network, we design two evaluation tasks including multi-view sketch correspondence, and pixel-wise retrieval. We compare our approach with the existing learning-based descriptors, including LeNet , L2-Net , HardNet , SOSNet  and AlexNet-based view pooling [20, 36] (AlexNet-VP in short). Note that we reimplemented LeNet, L2-Net, HardNet, and SOSNet following their original configurations. We also reimplemented AlexNet-VP and provide it with the same multi-scale patches as our network. The training input to all other networks are single-scale 3232 patches. For fair comparison, we only consider pixels which pass the AND-sampling criteria, i.e., the 32 32 patch of a multi-scale should be non-empty.
4.2.1 Sketch Correspondence
In this task we validate the performance of the learned descriptors in finding corresponding pixels in pairs of multi-view sketches in the test set. Given a pair of test sketches, for each pixel in one sketch, we compute its distances to all pixels in the other sketch (see distance visualization in Figure 6). We consider it as a successful matching if the pixel with the shortest distance is no further than 16 pixels (half of the smallest patch scale) away from the ground-truth pixel. Note that not all pixels in a sketch image have ground-truth correspondences (only among those projected). We report the averaged success rate as the correspondence accuracy.
The performance of of our approach and other competing methods on several representative categories is reported in Table 2. The detailed experimental results can be found in Table 7 in the appendix. It is observed that our network outperforms its competitors. Due to the lack of texture in sketch patches, the frameworks designed for image patches (i.e., L2-Net, HardNet and SOSNet) cannot learn effective descriptors to match the corresponding pixels in multi-view sketches. Our descriptor also surpasses those based on LeNet and AlexNet-VP. Figure 7 gives some qualitative comparisons between different approaches. Since 32 32 patches are required to be non-empty, test pixels are near sketch lines. We observe that the descriptors learned by LeNet, HardNet, L2-Net and SOSNet are less discriminative, and are thus not effective in finding corresponding pixels among multi-view sketches. AlexNet-VP uses a large input patch size of the 224
224, making it difficult to focus on local details in small regions. In addition, the max-pooling layer in AlexNet-VP may further decrease performance of the learned descriptors. As a consequence, AlexNet-VP produces more ambiguous distance maps (e.g., see the chair example in Figure 7) compared with our method. More correspondence results of multi-view sketches can be found in Figure 10.
4.2.2 Multi-view Pixel-wise Retrieval
We further design a multi-view corresponding pixel retrieval task. Given multi-view sketches synthesized from multiple shapes, we uniformly sample a set of pixels (10001600 pixels) on one sketch and search in the other sketches for the corresponding pixels which are from the same shape (in different views). We use the descriptors computed from the compared networks as queries and adopt the Mean Average Precision (MAP) to measure the retrieval performance. Experiments are performed category-wise in Structure-Recovery, PSB, and ShapeNet. Table 3 shows the results given by the compared methods. More detailed comparisons can be found in Table 8. In Tables 3 and 8, SketchDesc achieves the best performance among all the learned descriptors produced by the state-of-art learning-based methods on this task. Our learned descriptor surpasses the image-based descriptors of L2-Net, HardNet, and SOSNet by a large margin. For AlexNet-VP, it achieves a closer but still lower performance compared with our method.
4.2.3 View Disparity.
To further show the robustness of different learned descriptors against the degree of view disparity, given the same input test pixels in one sketch we visualize how the quality of correspondence inference changes with the increasing view disparity. As shown in Figure 8, SketchDesc shows a more stable performance of correspondence inference than the competitors. Please note that the ground-truth corresponding pixels might become invisible in certain views, while all the learned descriptors could not distinguish the visibility of corresponding pixels. Nevertheless, SketchDesc still produces the most reasonable results.
4.3 Ablation Study
In this subsection we validate the effectiveness of the key components in our method by conducting an ablation study.
The designed multi-scale patch-based representation () plays an essential role in our method. We first show how different scales can influence the performance of the learned descriptors. We feed our network with increasingly more scales and evaluate the performance on the pixel-wise retrieval task. We employ the average MAP (Mean Average Precision) metric over the whole dataset. Quantitative results are shown in Table 4. A representative visual comparison is shown in Figure 9 It is found that as larger scales are involved, the ambiguous regions (bright yellow regions) on feet, legs and backs of the camel are gradually rejected. In other words, by fed with the multi-scale patches, our network can enjoy not only a more precise local perception but also a global perspective.
|First scale ()||0.472||0.314||0.202|
|First 2 scales ()||0.695||0.570||0.484|
|First 3 scales ()||0.795||0.701||0.607|
|All 4 scales ()||0.819||0.727||0.660|
In our method the multi-scale patches are processed by a shared-weight scheme. To verify its effectiveness, we perform a comparison on the pixel-wise retrieval task with an unshared-weight network structure. The comparison results are reported in Table 5. It is found that the shared-weight structure in our network achieves a higher accuracy. The improvement is even more significant on PSB.
Training Data Generation
We evaluate the performance of two patch sampling mechanisms: OR-sampling and AND-sampling (Section 3.1). It can be found from Table 6 that OR-sampling achieves a significantly better performance. This is possibly because the OR-sampling leads to a significantly larger dataset for training our network.
4.4 Limitations and Discussions
Our method has several limitations. First, although our method could generalize well to unseen sketches or even hand-drawn sketches of the same objects, when the viewpoint differs from the examples in the training set drastically, our method could fail. This is a common generalization problem for any learning-based methods. Increasing the training data could help yet in the cost of additional training burden. We use a rather simple method to sample viewpoints for preparing the training data. A more careful view selection might be made by adopting best-view selection methods . Additionally, our method is currently designed for multi-view correspondences of rigid objects. If the object undergoes articulation or non-rigid deformations (e.g., people dancing), our method may not perform well. We consider this as an intriguing future work to explore.
In this paper, we have introduced a deep learning based method for correspondence learning among multiple sketches of an object in different views. We have proposed a multi-branch network which encodes contexts from multi-scale patches with global and local perspectives to produce a novel descriptor for semantically measuring the distance of pixels in multi-view sketch images. The multi-branch and shared-weights designs help the network capture more feature information from all scales of sketch patches. Our data preparation method provides the ground truth effectively for training our multi-branch network. We believe the generated data can benefit other applications. Both qualitative and quantitative experiments show that our learned descriptor is more effective than the existing learning-based descriptors. In the future, it would be interesting to exploit more neighboring information and learn the per-point features in a joint manner.
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