Dataset Information

Rotational-symmetry in a 3D scene and its 2D image.

ABSTRACT: A 3D shape of an object is N-fold rotational-symmetric if the shape is invariant for 360/N degree rotations about an axis. Human observers are sensitive to the 2D rotational-symmetry of a retinal image, but they are less sensitive than they are to 2D mirror-symmetry, which involves invariance to reflection across an axis. Note that perception of the mirror-symmetry of a 2D image and a 3D shape has been well studied, where it has been shown that observers are sensitive to the mirror-symmetry of a 3D shape, and that 3D mirror-symmetry plays a critical role in the veridical perception of a 3D shape from its 2D image. On the other hand, the perception of rotational-symmetry, especially 3D rotational-symmetry, has received very little study. In this paper, we derive the geometrical properties of 2D and 3D rotational-symmetry and compare them to the geometrical properties of mirror-symmetry. Then, we discuss perceptual differences between mirror- and rotational symmetry based on this comparison. We found that rotational-symmetry has many geometrical properties that are similar to the geometrical properties of mirror-symmetry, but note that the 2D projection of a 3D rotational-symmetrical shape is more complex computationally than the 2D projection of a 3D mirror-symmetrical shape. This computational difficulty could make the human visual system less sensitive to the rotational-symmetry of a 3D shape than its mirror-symmetry.

SUBMITTER: Sawada T

PROVIDER: S-EPMC6591714 | biostudies-literature | 2018 Dec

REPOSITORIES: biostudies-literature

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Rotational-symmetry in a 3D scene and its 2D image.

Sawada Tadamasa T Zaidi Qasim Q

Journal of mathematical psychology 20181120

A 3D shape of an object is <i>N</i>-fold rotational-symmetric if the shape is invariant for 360/<i>N</i> degree rotations about an axis. Human observers are sensitive to the 2D rotational-symmetry of a retinal image, but they are less sensitive than they are to 2D mirror-symmetry, which involves invariance to reflection across an axis. Note that perception of the mirror-symmetry of a 2D image and a 3D shape has been well studied, where it has been shown that observers are sensitive to the mirror ...[more]

PMID: 31239585

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Project description:Surgical reduction of pelvic dislocation is a challenging procedure with poor long-term prognosis if reduction does not accurately restore natural morphology. The procedure often requires long fluoroscopic exposure times and trial-and-error to achieve accurate reduction. We report a method to automatically compute the target pose of dislocated bones in preoperative CT and provide 3D guidance of reduction using routine 2D fluoroscopy. A pelvic statistical shape model (SSM) and a statistical pose model (SPM) were formed from an atlas of 40 pelvic CT images. Multi-body bone segmentation was achieved by mapping the SSM to a preoperative CT via an active shape model. The target reduction pose for the dislocated bone is estimated by fitting the poses of undislocated bones to the SPM. Intraoperatively, multiple bones are registered to fluoroscopy images via 3D-2D registration to obtain 3D pose estimates from 2D images. The method was examined in three studies: (1) a simulation study of 40 CT images simulating a range of dislocation patterns; (2) a pelvic phantom study with controlled dislocation of the left innominate bone; (3) a clinical case study investigating feasibility in images acquired during pelvic reduction surgery. Experiments investigated the accuracy of registration as a function of initialization error (capture range), image quality (radiation dose and image noise), and field of view (FOV) size. The simulation study achieved target pose estimation with translational error of median 2.3 mm (1.4 mm interquartile range, IQR) and rotational error of 2.1° (1.3° IQR). 3D-2D registration yielded 0.3 mm (0.2 mm IQR) in-plane and 0.3 mm (0.2 mm IQR) out-of-plane translational error, with in-plane capture range of ±50 mm and out-of-plane capture range of ±120 mm. The phantom study demonstrated 3D-2D target registration error of 2.5 mm (1.5 mm IQR), and the method was robust over a large dose range, down to 5 [Formula: see text]Gy/frame (an order of magnitude lower than the nominal fluoroscopic dose). The clinical feasibility study demonstrated accurate registration with both preoperative and intraoperative radiographs, yielding 3.1 mm (1.0 mm IQR) projection distance error with robust performance for FOV ranging from 340 × 340 mm2 to 170 × 170 mm2 (at the image plane). The method demonstrated accurate estimation of the target reduction pose in simulation, phantom, and a clinical feasibility study for a broad range of dislocation patterns, initialization error, dose levels, and FOV size. The system provides a novel means of guidance and assessment of pelvic reduction from routinely acquired preoperative CT and intraoperative fluoroscopy. The method has the potential to reduce radiation dose by minimizing trial-and-error and to improve outcomes by guiding more accurate reduction of joint dislocations.

Dataset Information

Rotational-symmetry in a 3D scene and its 2D image.

Publications

Rotational-symmetry in a 3D scene and its 2D image.

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