Globally Optimal Pose from Orthographic Silhouettes

Agniva Sengupta; Dilara Kuş; Jianning Li; Stefan Zachow

cs.CVApr 10, 2026

Globally Optimal Pose from Orthographic Silhouettes

Authors: Agniva Sengupta, Dilara Kuş, Jianning Li, Stefan Zachow

Organizations: Freie Universität Berlin · Zuse Institute Berlin

Abstract

We solve the problem of determining the pose of known shapes in $\mathbb{R}^3$ from their unoccluded silhouettes. The pose is determined up to global optimality using a simple yet under-explored property of the area-of-silhouette: its continuity w.r.t trajectories in the rotation space. The proposed method utilises pre-computed silhouette-signatures, modelled as a response surface of the area-of-silhouettes. Querying this silhouette-signature response surface for pose estimation leads to a strong branching of the rotation search space, making resolution-guided candidate search feasible. Additionally, we utilise the aspect ratio of 2D ellipses fitted to projected silhouettes as an auxiliary global shape signature to accelerate the pose search. This combined strategy forms the first method to efficiently estimate globally optimal pose from just the silhouettes, without being guided by correspondences, for any shape, irrespective of its convexity and genus. We validate our method on synthetic and real examples, demonstrating significantly improved accuracy against comparable approaches. Code, data, and supplementary in: https://agnivsen.github.io/pose-from-silhouette/

Figures & tables

Figure 1: When a L- c trajectory from A to B on an unit sphere (a) is mapped to $\mathbb{SO}(3)$ and applied to two arbitrary shapes (b,c), the resulting evolution of orthographic A o S , as shown in (d,e) with its abscissa mapped as $[A,B]\mapsto[0,1]$ , is L- c

Figure 2: (a) Shows the Postel ball ( $\mathcal{S}_{\pi}$ ) and disc ( $\mathcal{D}_{\pi}$ ) inside a cube of length $\pi$ with axes $(X_{\pi},Y_{\pi},Z_{\pi})$ , (b) shows the 3D template of PD , (c) shows the mapping of $\mathcal{D}_{\pi}$ to A o S for PD , and (d) shows the mapping of $\mathcal{D}_{\pi}$ to elliptical aspect ratio for PD

Figure 3: Example of pose estimation: (a) shows input silhouette from PD , (b) shows $U_{\mathcal{A}}$ in black-dashes, $U_{\mathscr{E}}$ in blue, and $U_{\mathcal{A}\cap\mathscr{E}}$ in red on $\mathcal{D}_{\pi}$ , and (c) shows $\tilde{C}$ in black and the G t pose in red (encircled) inside $\mathcal{S}_{\pi}$ ; the PARS and PEARS for PD are given in Fig. 2

Figure 4: Success rate of pose estimation across the seven best solution candidates, denoted C

x

(

x\in[1,7]

), including some failure cases only for ‘high’ noise

Figure 5: RMSE (top-row) and runtime (bottom-row) of GlOptiPoS under varying (a)

\epsilon_{z}

, (b)

\epsilon_{\cap}

, and (c)

P

. Blue curves denote interpolated mean-curves (please zoom-in).

Panel of Figure 6 — Figure 6: I) The six shapes A through F using spherical harmonics, and II) $|\tilde{C}|$ plotted against shapes A through F , the red curve passes through mean values, the shaded area gives the range

Figure 7: Qualitative results on the asymmetric shapes from complex_movable_handheld sequence of B c OT dataset: Ape , Cat , Jack , Squirrel , Stitch , and Vampire queen shown in (A) through (F); red curves are G t silhouettes, blue curves are from GlOptiPoS Π + (please zoom-in for details)

Object Pose Estimation

Object pose estimation recovers an object's 3D position and orientation from images, depth, point clouds, or contact sensing.

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This paper presents a new algorithm to estimate absolute camera pose given an axis of the camera's rotation matrix. Current algorithms solve the problem via algebraic solutions on limited input domains. This paper shows that the problem can be solved efficiently by finding the intersection points of a hyperbola and the unit circle. The solution can flexibly accommodate combinations of point and line features in minimal and overconstrained configurations. In addition, the two special cases of planar and minimal configurations are identified to yield simpler closed-form solutions. Extensive experiments validate the approach.

Abstract

Object Pose Estimation

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