Articulate Anything: Open-vocabulary 3D Articulated Object Generation

Q8: In Table 2, the "Ours" score in the last column is significantly higher than that of PartNet-Mobility, which I assume serves as a ground-truth reference. Could you clarify why this is the case?

As previously discussed, objects in PartNet-Mobility serve as ground truth for kinematic structure. However, in terms of rendering quality, they are synthetic and feature simple textures and materials. In contrast, the 2D diffusion model used during optimization is trained on rendered views of Objaverse objects, which exhibit higher visual quality compared to PartNet-Mobility objects. This allows the optimized texture to appear more visually plausible than that of PartNet-Mobility objects.

Furthermore, Richdreamer optimizes a Physically Based Rendering (PBR) material model, further enhancing visual quality. For instance, the safe in Figure 5 has a metallic surface, while the drawer in Figure 4 appears wooden. These factors collectively contribute to the higher scores achieved. However, when comparing textureless renderings (columns 3 and 4 in Table 2), the score of Articulate Anything no longer surpasses that of PartNet-Mobility.

Q9: In Table 2, the VQA score for NAP is also higher than “PartNet w/o texture”. What is it implied?

NAP retrieves part meshes from PartNet-Mobility and only slightly exceeds PartNet w/o texture in performance. We believe this small difference is likely due to random fluctuations.

Q10: In Figure 3, what is the input to each method and how are the examples selected for comparison?

The input to each method (NAP, CAGE, URDFormer) is the same as in the unconditional generation setting. The examples are selected randomly.

Q11: On the side of articulation estimation, it is possible to compare it with other methods beyond just NAP and CAGE, such as Shape2Motion and Real2Code.

We have added comparisons with ANCSH and OPD for articulation estimation, with the results presented in General Response Section 2C. Since Shape2Motion does not provide a checkpoint trained on PartNet-Mobility, we selected two more recent works, ANCSH and OPD, which offer trained checkpoints. As for Real2Code, their finetuned LLM checkpoint and inference code have not been released, so we cannot make a comparison.

Q12: Missing references

Thanks for the reminder. We have incorporated the missing citations into our paper.

We wish that our response has addressed your concerns, and turns your assessment to the positive side. If you have any more questions, please feel free to let us know during the rebuttal window.

Best,

Authors

Questions:

Q1: How is the GPT4o exactly prompted for the task of part segmentation and joint point selection?

Please refer to Appendix F: Prompting Details.

Q2: Once the joint point is selected, how are the joint limit and the direction of rotation/translation determined?

A rotation axis has six unknowns and requires at least two points in 3D space or one point plus a directional vector to define it deterministically. (If more than two points are available, a line is fitted through them.) A translation axis, having three unknowns, requires only a directional vector to define it.

For revolute joints, we incrementally rotate the child link based on the joint parameters and identify the maximum range where penetration remains below a predefined threshold. For prismatic joints, we follow the joint limits provided by GPT4o.

For details on determining the joint axis, refer to Appendix F: Prompting Details, paragraph Articulation Parameter Estimation, substep 3. For determining the joint limit, refer to substep 4 of the same paragraph.

Q3: How is the SDF of each part computed in section 3.3?

The 3D segmentation step generates a segmented point cloud for each part. For each part, the Signed Distance Function (SDF) of the mesh corresponding to its segmented 3D point cloud is computed. Then, for points outside the part, their SDF values are evaluated. Points with SDF values below a predefined threshold are identified as the connected area.

For further detail, please refer to Appendix F: Prompting Details, paragraph Articulation Parameter Estimation, substep 1.

Q4: How is the optimization process implemented? Where is the text prompt from? How many iterations are required to optimize each object? How long does it take?

We have included the detailed implementation of the optimization process in General Response Section 4A.

In the quantitative experiments, the text prompt used is simply "a OBJECT_CATEGORY_NAME," while the text prompts for qualitative results (Figures 4, 5, and 9) are manually specified. Geometry refinement requires 1,000 iterations, and texture refinement takes 1,600 iterations. Using a single A100 GPU with a rendering resolution of 1024x1024, geometry refinement takes approximately 50 minutes, and texture refinement takes 90 minutes.

Q5: For unconditional generation, how is the experiment conducted? What are the input to this method and other baselines (NAP, CAGE, URDFormer)? Did you retrain URDFormer on the same split as CAGE?

NAP takes no input. CAGE requires a connectivity graph and an object category label as input. URDFormer takes an image as input. Articulate Anything takes a text input, specifically the object category name. For more details of the experimental setup of unconditional generation, including the inputs for Articulate Anything and other baseline methods, please refer to General Response section 4B.

As URDFormer has not released their training code, we used the checkpoint they provided.

Q6: What do the red and blue boxes mean in Figure 5? Is the object shown at the left-most the input?

The boxes are intended to demonstrate that the semantic features of parts are preserved across different text prompts during the refinement stage. The object shown at the left-most is a visualization of part segmentation, not the input.

Q7: For the comparison of articulation parameter estimation, what is the input to NAP and CAGE? How are they implemented to be compared?

For NAP, ground truth vertices (e.g., part bounding boxes, spatial locations, shape latents) are provided, while edges (joint parameters) are estimated. For CAGE, some attributes of each node, such as bounding boxes, joint types, and semantic labels, are provided, while others, including joint axes and ranges, are estimated. We use the official implementations of NAP and CAGE from their respective GitHub repositories. More details about the comparison of articulation parameter estimation is described in General Response section 3B.

Thank you for your insightful and constructive comments! We have added additional experiments and modified our paper according to your comments.

1. Somewhat misleading presentation

Thank you for pointing out the inconsistency between the task proposed in our paper and its presentation. We acknowledge that the primary goal of Articulate Anything is to convert a rigid mesh into its articulated counterpart. The refinement step is an additional process designed to make our pipeline complete when the input mesh is a surface mesh. We believe this refinement step aligns with the goal of converting a rigid mesh into its articulated counterpart because, although it modifies the geometry and texture of the input surface mesh, it preserves the semantic parts and articulation parameters. Since our ultimate goal is to collect large-scale, realistic articulated object data for robotics and embodied AI, preserving the geometry and texture is not essential, particularly when they are low-quality or unrealistic.

Additionally, open-vocabulary articulated object generation represents a novel downstream task enabled by our pipeline. This is achieved by leveraging a 3D generation model to create 3D surface meshes as inputs for Articulate Anything. The unconditional experiments were conducted to evaluate the end-to-end performance of our pipeline.

With these clarifications, we have reformed our paper to make it more self-contained and aligned with its core objectives.

2. No quantitative evaluation of the reconstruction quality

As discussed earlier, our goal is to collect large-scale, realistic articulated object data for robotics and embodied AI. Therefore, we prioritize preserving articulation parameters and part semantics over the low-quality geometry and texture of generated surface meshes. Guided by this perspective, we evaluate the refinement step using metrics that assess the visual quality and realism of refined objects, rather than reconstruction accuracy.

While objects in PartNet-Mobility can serve as ground truth for articulation parameters and part semantics, they are synthetic in terms of rendering quality, with simplistic textures, materials, and shapes. Additionally, the diversity of objects in PartNet-Mobility is limited. As a result, we believe that PartNet-Mobility objects cannot be used as ground truth for geometry and texture. The goal of our pipeline is not to fit the distribution of PartNet-Mobility but to go beyond existing datasets and collect realistic articulated objects.

Therefore, we use image-based scores rather than metrics like ID, which measure the distance between our collected objects and those from PartNet-Mobility. For articulation parameters and part semantics, we conducted additional experiments to compare articulation parameter estimation performance with methods focused on this task, such as ANCSH and OPD. The results are detailed in General Response Section 3B.

3. Missing Technical and Experimental Details

To enhance clarity and reproducibility, we have expanded our appendix with the following sections:

• Section C: Details of the Refinement Step: This section provides a comprehensive description of the refinement step.
• Section D: Experiment Settings: Here, we clarify the experimental setups for articulation parameter estimation and unconditional generation, including the inputs and outputs for both baseline methods and our method, which ensures fair comparison.
• Section F: Prompting Details: This section includes the exact prompts used for GPT-4 and outlines the detailed substeps for the 3D segmentation and articulation parameter estimation steps.

4. Low resolution of Qualitative Results

Thank you for the reminder. We have updated the figures with high-resolution versions to improve clarity and presentation quality.

Thank you for your insightful and constructive comments! We have added additional experiments and modified our paper according to your comments.

1. The manuscript in Part C is too rough

Thank you for pointing this out. We have provided a detailed explanation of the refinement step in General Response Section 4A, including mathematical equations and pseudocode for clarity. Additionally, we conducted a quantitative ablation study on the refinement step and included more visualizations comparing objects before and after refinement.

In the quantitative ablation study, we test the following settings: 1. No refinement step applied. 2. Refinement step applied without random transformation (same as Richdreamer). 3. Refinement step applied with random transformation. The results are summarized in the table below.

We also included additional qualitative results to illustrate the differences in geometry before and after refinement. These results can be viewed at the following link: https://drive.google.com/file/d/1Q7B2Z1WIocCE0saN2ggZvniGu3gDGO2q/view?usp=drive_link. For more details, please refer to General Response Section 3C and 3D.

2. Provide examples of cases where the pipeline fails or produces suboptimal results

Visualizations of some failure cases can be found at the following link: https://drive.google.com/file/d/11l73OxPfDN9ZjT4GENErR2AeO1gHVFuR/view?usp=drive_link. In the first case, the refinement step mistakenly optimized a transparent glass door of a dishwasher and hallucinated dishes behind the door. This issue sometimes arises due to the randomness in the optimization process and the fact that the SDS loss for texture is computed in RGB space, which limits the albedo diffusion model’s understanding of explicit 3D structures. In the second case, inaccurate 3D segmentation of a plug resulted in artifacts. Since the current 3D segmentation step is not completely accurate, incorrect segmentation results can negatively affect subsequent steps. Therefore, Articulate Anything would benefit from a stronger open-vocabulary 3D segmentation model. Progress in segmentation models could significantly enhance the overall performance of Articulate Anything, addressing these limitations and reducing failure cases.

Questions:

Q1: Combine Figures 4, 5, and 6 into a single, more comprehensive figure Add labels or annotations to highlight key features or differences between examples Include a diverse set of objects to better showcase the method's capabilities.

Thank you for the advice. We have combined these figures and added captions to explain the results in the revised figure. Additionally, we have included more results from our pipeline in Appendix Sections B and E.

Q2: Comparision between the improvement in Part C and baseline method is missing.

As our refinement step is developed over Richdreamer, we use it as the baseline for the refinement step. We report scores for the following settings: 1. No refinement step applied. 2. Refinement step applied without random transformation (same as Richdreamer). 3. Refinement step applied with random transformation. The results are summarized in the table below.

For more details please refer to General Response Section 3C and 3D.

We wish that our response has addressed your concerns, and turns your assessment to the positive side. If you have any more questions, please feel free to let us know during the rebuttal window.

Best,

Authors

2. Please provide more discussions on such details and show more quantative results on this part.

We observed that SAM provides inconsistent segmentation across different views, along with varying granularity. Additionally, SAM tends to over-segment, with segmentation granularity that is typically finer than that of a semantic part. Leveraging this observation, we designed two merging steps to transform the 2D segmentation masks from SAM into 3D segmentation masks of semantic parts.

The first merging step merges 2D segmentation masks across different views into 3D segmentation masks based on overlap ratios. The semantics of each 3D mask are determined by the most frequent semantic label among its 2D mask components.

The second merging step further combines adjacent 3D segmentation masks with the same semantics. To prevent merging different instances of the same semantic part (e.g., two adjacent drawers), we prompt GPT4o to differentiate instances within the same semantic category.

Part labels are generated using GPT4o. We simply provide rendered RGB images as input to GPT4o and ask it to identify semantic parts.

For quantitative evaluation, we conducted experiments to compare the segmentation step of Articulate Anything with PartSlip and PartDistill. Results in the previous table clearly demonstrate our advantage over both baselines. Details are provided in General Response Section 3A. These results further validate that by properly utilizing large foundation models like SAM and GPT4o, we achieve superior segmentation performance compared to methods relying on less capable pretrained models.

3. Please provide a more detailed explanation on the input of different methods of the comparison and explain why the comparison is fair if the proposed method uses an existing 3D mesh. Please also discuss how to fetch the 3D mesh to compare with other methods.

In the unconditional generation experiment, all input meshes for Articulate Anything are generated using InstantMesh, an image-to-3D generative model. The input images for InstantMesh are created using Stable Diffusion, conditioned on text prompts corresponding to object category names. We do not use existing meshes from datasets or websites for the unconditional generation experiments. In contrast, NAP and CAGE source their parts from the PartNet-Mobility dataset, which consists of pre-existing meshes. Therefore, we believe this comparison is fair, if not slightly biased in favor of NAP and CAGE.

Questions

Q1: For the shape in the teaser image and in the website, do they go through the refinement step? Seems that their geometry is much better than the results after the refinement step in the paper. Please give more clarification on the process to generate the demos of the objects shown in the teaser image on how do they keep the original texture, if they go through the whole pipeline of the proposed method?

The objects featured in our teaser are sourced from Objaverse (as metioned in the caption of figure 1) and do not undergo the refinement step. As described in the "Annotate 3D Object Datasets" section of the Applications, we only apply the 3D segmentation and articulation estimation steps of our pipeline to annotate objects retrieved from Objaverse. TThe refinement step is specifically designed for surface meshes with incomplete part geometry. Given the current limitations of recent 3D generation methods (e.g., SDS optimization and others), their output still falls significantly short of artist-crafted meshes. Consequently, it is not optimal to apply the refinement step to artist-crafted meshes, particularly those with complete part geometry and inner structure.

We wish that our response has addressed your concerns, and turns your assessment to the positive side. If you have any more questions, please feel free to let us know during the rebuttal window.

Best,

Authors

Thank you for your insightful and constructive comments! We have added additional experiments and modified our paper according to your comments.

1. This paper is not an articulated object generation work.... There needs to be comparisons with them on the segmentation and motion prediction performance (e.g. Category-Level Articulated Object Pose Estimation, PartSLIP).

As stated in General Response Section 2, we sincerely appreciate your feedback in helping us clarify the primary task of our pipeline, and we have revised our paper accordingly. Previously, we regarded our pipeline as generative because, by integrating an exisitng 3D generation model to generate surface meshes as the input to Articulate Anything, our pipeline takes advanatge of the open-vocabulary 3D generation capabilities of the 3D generation model and inherits its generative paradigm. Additionally, we aimed to evaluate the performance of Articulate Anything in an end-to-end manner and compare it with other state-of-the-art methods. After the reform, we no longer consider Articulate Anything as a generative framework. Instead, we view open-vocabulary articulated object generation as a novel downstream task enabled by our pipeline. Under this perspective, we included quantitative experiments to evaluate the performance of 3D segmentation and articulation parameter estimation, comparing against other open-vocabulary 3D segmentation methods and motion prediction works.

For 3D segmentation, we use PartSlip and PartDistill as baselines and conduct evaluation on the PartNetE dataset. The results are presented in the table below. For details regarding the experimental setup, please refer to General Response Section 3A.

For articulation parameter estimation, we initially compared against NAP and CAGE, as these two generative methods can produce joint configurations conditioned on complete part geometries, which closely aligns with the input to our articulation parameter estimation step. We now additionally include ANCSH and OPD as baselines, using single-observation RGB-D input. The results are reported in the table below.

Experimental results show that Artiulate Anything performs better than NAP and CAGE. For details of the experimental setup, please refer to General Response section 3B.

Thank you for your insightful and constructive comments! We have added additional experiments and modified our paper according to your comments.

1. Novelty: While the method is reasonable, it essentially relies on the power of various large models and diffusion models, which may limit the novelty of the proposed framework.

We use large models and diffusion models over existing pretrained models to leverage the vast knowledge embedded in these models for achieving open-vocabulary mesh-to-articulated-object conversion—a novel task that has not been addressed before.

Effectively utilizing large models for complex tasks is non-trivial and requires innovation, as the process of extracting their knowledge is not straightforward. For example, you cannot simply input an image into GPT4o and expect per-pixel segmentation masks; instead, you need to pre-segment the image and label each part using techniques like SoM. Similarly, GPT4o cannot directly process a 3D mesh; instead, you must design visual prompts that accurately map back to the 3D domain without ambiguity. In conclusion, we believe that Articulate Anything demonstrates significant novelty in addressing these challenges.

2. Writing: Some parts of this paper are difficult to follow

Thank you for pointing out the writing issues in our paper. We have provided a detailed explanation of the refinement step in General Response Section 4A, including mathematical equations and pseudocode to clarify the process. Additionally, the prompting details for the 3D segmentation and articulation estimation steps are included in Appendix Section F for further clarification.

3. Experiments: In the ablation study, it is recommended to add more quantitative experiments to evaluate the performance of different components of the proposed framework

We compare three different settings to validate the effectiveness of refinement step: 1. No refinement step applied. 2. Refinement step applied without random transformation (same as Richdreamer). 3. Refinement step applied with random transformation. The results are presented in the table below. The highest scores are achieved when using refinement with random transformation, demonstrating the effectiveness of our refinement step.

4. Performance: The performance of the proposed method is not particularly impressive.

It is worth noting that Articulate Anything generates articulated objects in an open-vocabulary manner, whereas NAP and CAGE are restricted to specific categories of articulated objects based on their training datasets. The experiments for articulation parameter estimation were conducted on object categories that NAP and CAGE were trained on. While the performance of Articulate Anything on these specific categories is comparable to CAGE, its range of operable categories is significantly broader. Unlike NAP and CAGE, which is not able to operate on unseen categories, Articulate Anything does not have such concern.

For unconditional generation, CAGE represents parts using axis-aligned bounding boxes and subsequently retrieves parts from the PartNet-Mobility dataset. This approach imposes an additional limitation on CAGE, as the number of parts available in PartNet-Mobility is inherently restricted.

The most significant advantage of Articulate Anything over existing methods is that it is an open-vocabulary approach that does not require any labeled articulated object data. It is capable of generalizing to a broad range of object categories, overcoming the limitations of category-specific models like NAP and CAGE.

We wish that our response has addressed your concerns, and turns your assessment to the positive side. If you have any more questions, please feel free to let us know during the rebuttal window.

Best,

Authors

[1] Liu, Minghua, et al. "Partslip: Low-shot part segmentation for 3d point clouds via pretrained image-language models." Proceedings of the IEEE/CVF conference on computer vision and pattern recognition. 2023.

[2] Jiang, Hanxiao, et al. "OPD: Single-view 3D openable part detection." European Conference on Computer Vision. Cham: Springer Nature Switzerland, 2022.

[3] Li, Xiaolong, et al. "Category-level articulated object pose estimation." Proceedings of the IEEE/CVF conference on computer vision and pattern recognition. 2020.\

[4] Jiang, Hanxiao, et al. "OPD: Single-view 3D openable part detection." European Conference on Computer Vision. Cham: Springer Nature Switzerland, 2022.

[5] Umam, Ardian, et al. "PartDistill: 3D Shape Part Segmentation by Vision-Language Model Distillation." Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. 2024.

4. Implementation Details

• [A] The Refinement Step. In Richdreamer[4], the Score Distillation Sampling process proposed by DreamFusion is formulated as follows: Given a 3D representation $\phi$, and a differentiable renderer $g$, the rendered image is $x = g(\phi)$. The SDS loss is then used to optimize the 3D representation $\phi$: $\nabla_{\phi} \mathcal{L}\_{\text{SDS}}(\phi, x=g(\phi)) = \mathbb{E}\_{t, \epsilon}\left[w(t)(\epsilon\_{\theta}(z\_t ; y, t) - \epsilon) \frac{\partial x}{\partial \phi}\right]$, where $z_t$ is the noisy latent code, $\epsilon$ is the injected noise and $\epsilon_\theta$ is the noise predicted by a denoising model $\theta$, conditioned on timestep $t$ and text embedding $y$. The term $w(t)$ is a timestep dependent weighting factor. In Richdreamer and other previous works the 3D representation $\phi$ is static, whereas in our case, it is articulated. Omitting other attributes, we denote the 3D representation of articulated objects as $\phi_q$, where $q$ is a vector representing joint positions. During optimization, the base of the articulated object remains fixed. Since non-fixed joints of interest (revolute, prismatic, and continuous) all have one degree of freedom, each element in $q$ corresponds to the position of a non-fixed joint in $\phi_q$. The articulated object in its rest configuration is denoted as $\phi_{q_0}$. A transformation function $T$ maps $\phi_{q_0}$ to $\phi_q = T(\phi_{q_0}, q)$ given the desired joint positions $q$. The optimization process for Richdreamer and other previous SDS optimization methods can be briefly summarized by the following pseudo-code:

FOR i IN iterations:
    render an image x (x = g(phi))
    sample timestep t
    compute SDS loss
    update optimizer

In our approach, we extend this process by sampling joint positions and transforming object parts accordingly:

FOR i IN iterations:
    sample joint position q
    transform parts according to q (phi_q = T(phi_q0, q))
    render an image x (x = g(phi_q))
    sample timestep t
    compute SDS loss
    update optimizer

• [B] Experiment Setup. Articulation parameter estimation: We use objects from CAGE's test split. In our setup, the shapes of the testing objects are known, and articulation parameters are predicted. For NAP, ground truth vertices (e.g., part bounding boxes, spatial locations, shape latents) are provided, while edges (joint parameters) are estimated. Since NAP uniformly represents all joints using Plücker coordinates, we evaluate only the translational component for prismatic joints and the rotational component for revolute joints. For CAGE, some attributes of each node, such as bounding boxes, joint types, and semantic labels, are provided, while others, including joint axes and ranges, are estimated. In Articulate Anything, the shapes, semantics of each part, and joint types are given, and the joint axes and limits are estimated. Unconditional Generation: We generate articulated objects using minimal input. For NAP, no conditions are provided; its diffusion model generates objects unconditionally. After generation, the initial shape is decoded from the generated shape latent and replaced by the nearest matching part mesh. For CAGE, a random articulated object from PartNet-Mobility, in CAGE's test split, is retrieved. Its connectivity graph and object category label are used as input to CAGE's diffusion model. After generating bounding boxes, part semantics, and joint parameters, part meshes are retrieved using CAGE's retrieval method. For URDFormer, an object category is randomly sampled, and an image is generated using Stable Diffusion 3 (prompted to produce a front-view image of an object in the sampled category with a white background). URDFormer then takes the generated image as input and outputs a URDF. In Articulate Anything, an image is generated similarly, followed by mesh generation using InstantMesh. The generated mesh is processed through the full pipeline of Articulate Anything to produce an articulated object. For PartNet-Mobility, objects in the relevant categories are randomly retrieved. For each generated object, we render eight views surrounding it and compute the CLIPScore and VQAScore. The input text for these scores is "a OBJECT_CATEGORY".

• [C] Prompting Details. Please refer to appendix section G prompting details.

• [D] Qualitative Ablation Study for Refinement Step. We also provide visualizations of the input and output of the refinement step, as shown in the link: https://drive.google.com/file/d/1Q7B2Z1WIocCE0saN2ggZvniGu3gDGO2q/view?usp=drive_link. The pencil case and lighter in the second and third rows feature manually set joint parameters and shape primitives as link geometries. The refinement step successfully optimizes storage space for the drawer and pencil case and generates a nozzle structure for the lighter, and produces plausible textures.

3. New Experiments

• [A] Quantitative comparison for 3D Segmentation. We compare the semantic segmentation performance of the segmentation component in Articulate Anything to the zero-shot version of PartSlip[1] and PartDistill[5]. The comparison focuses on object categories from the PartnetE dataset proposed by PartSlip. Each object category in PartNetE has predefined part labels, and we adhere to this setup, evaluating segmentation performance exclusively on these predefined parts. For PartSlip and PartDistill, the input is a multi-view fusion point cloud generated by projecting RGB-D pixels from rendered images into 3D space, and the output is a semantic label for each point in the input point cloud. For Articulate Anything, the input is a 3D surface mesh. It then undergoes the 3D segmentation step, producing a labeled point cloud as output. The predicted point cloud segmentation is then compared with the ground-truth segmentation, and mIOU is measured. The results, shown in the table below, demonstrate that the segmentation component of Articulate Anything outperforms PartSlip and PartDistill overall.

• [B] Articulation Parameters Estimation. We compare Articulate Anything with other methods focused on articulation estimation. For OPD[2], we use the official GitHub repository and the RGB-D input checkpoint. For ANCSH[3], we use the PyTorch implementation provided by OPD's authors. The evaluation is conducted on the "Onedoor" dataset, a subset of OPDsynth, which includes objects from various categories in PartNet-Mobility that feature doors. This dataset is used to train ANCSH in its pytorch implementation. ANCSH uses a single-view point cloud as input, while OPD uses an RGB image (with optional depth information). Both methods output the segmentation of relevant parts and their joint parameters. To ensure a fair comparison, our pipeline is adapted to the single-observation RGB-D setting: only one image (the input observation) undergoes segmentation, and the results are directly projected as a point cloud with segmentation labels. This single-view point cloud is then processed in the second step for articulation parameter estimation. The results, shown in the table below, demonstrate that Articulate Anything outperforms both ANCSH and OPD, even when evaluated in-domain.

• [C] Quantitative Ablation Study for Refinement Step. In the ablation study, we evaluate the same objects used in the quantitative evaluation of unconditional generation. We apply three different settings to the intermediate output of the articulation estimation step: 1. No refinement step applied. 2. Refinement step applied without random transformation (same as Richdreamer). 3. Refinement step applied with random transformation. The results are presented in the table below. The highest scores are achieved when using refinement with random transformation, demonstrating the effectiveness of our refinement step.