Recovering Black-Box Point Cloud Models from Pose Shifts via Derivative-Free Optimization

Pretrained vision models often misclassify inputs that are rotated, scaled, or sheared, even though these affine transformations leave the object class unchanged. Robustness is usually restored either by building equivariance into the architecture or by retraining with augmentation, both of which require changing or retraining the model. Test-time canonicalization instead leaves the classifier untouched. It undoes the transformation of each input, mapping it to a canonical form near the training distribution before classification. Existing canonicalizers, however, rely on a narrow set of logit-based energy scores and bespoke search procedures, leaving the design space of scoring functions and optimizers unexplored. We reframe canonicalization as out-of-distribution (OOD) detection, which lets any OOD score serve as the energy minimized over transformations. Across benchmarks ranging from handwritten characters and sketches to natural images and 3D point clouds, we systematically evaluate around twenty OOD scores and nine search algorithms, finding that distance-based scores paired with random search and local refinement perform best overall. Because canonicalizing an already-aligned input can hurt accuracy, we add a gated mechanism that transforms an input only when its OOD score indicates this is needed, preserving most in-distribution accuracy while retaining the robustness gains on transformed inputs. Code is available at github.com/johschm/its.

Canonicalization resolves the rotational and permutation ambiguity of 3D point clouds by selecting a unique orbit representative, maintaining their geometric information while allowing standard architectures, such as Transformers, to operate on them. Existing canonicalizations, however, exhibit discontinuity jumps on molecular configurations and non-trivial invariance errors in popular molecular datasets, which lead to ambiguity in their representation. To bridge this gap, we introduce LexiCan, a canonicalization that is provably invariant under either $O(3)$ or $SO(3)$, empirically invariant to rotations to within $\sim 10^{-6}$ angstroms on the QM9 and QM-sym molecular datasets, and mitigates discontinuity jumps on QM-sym, while running orders of magnitude faster than an existing canonicalization. Finally, non-invariant models perform better on QM9 property prediction and ModelNet40 shape classification with LexiCan than with that canonicalization.

Semantic segmentation of aerial point cloud is trapped in a generalization crisis under distinct domain shifts. While test-time adaptation offers a privacy-preserving and computationally efficient way to adapt pre-trained models to unlabeled target-domain data during inference, existing methods, bound to closed-set label assumptions and non-scalable point-wise segmentation pipelines, still struggle with semantic shifts. We ask: can we adapt any given pre-trained aerial point cloud segmentation model to a shifted target domain at the inference phase alone, without additional training, while segmenting target-specific categories beyond the source label space on demand? This paper introduces COSTA, which breaks this limitation by shifting from closed-set point-wise adaptation to cluster-centric open-set semantic propagation. Our core discovery is that, once effectively adapted at test time, the rich feature distribution of aerial point clouds can be distilled into a compact set of well-separated semantic centroids that are transferable across label spaces. COSTA leverages this to reformulate open-set semantic segmentation as a cluster-level propagating process: it first bridges the domain gap through proven test-time adaptation, then groups each batch of target-domain points into a small set of semantic clusters based on the similarity distribution in the adapted feature space, and finally propagates high-confidence pseudo labels obtained from an open-vocabulary vision-language model to all points through cluster-level voting. This cluster-centric paradigm enables test-time adaptation of aerial point clouds under significant domain gaps with mixed semantic shifts. With DALES as the source domain, COSTA enables on-demand segmentation across three aerial point cloud benchmarks with distinct domains and heterogeneous category spaces, achieving up to 70.09% mIoU under this new setting.