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The deformable registration of a preoperative organ volume to an intraoperative laparoscopy image is required to achieve augmented reality in laparoscopy. This is an extremely challenging objective for the liver. This is because the preoperative volume is textureless, and the liver is deformed and only partially visible in the laparoscopy image. We solve this problem by modeling the preoperative volume as a Neo-Hookean elastic model, which we evolve under shading and contour cues. The contour cues combine the organ’s silhouette and a few curvilinear anatomical landmarks. The problem is difficult because the shading cue is highly nonconvex and the contour cues give curve-level (and not point-level) correspondences. We propose a convergent alternating projections algorithm, which achieves a \(4\%\) registration error.

This paper proposes a new method for describing parenchymatous organs by the set of volumetric primitives with simple shapes. The proposed method is based on our modified Self-organizing Deformable Model (mSDM) which maps an object surface model onto a target surface with no foldovers. By extending mSDM to apply to organ volume models, the proposed method, volumetric SDM (vSDM), finds the one-to-one correspondence between the volume model and its target volume. During the mapping, vSDM preserves geometrical properties of the original model while mapping internal structures of the model onto their corresponding primitives inside of the target volume. Owing to these characteristics, vSDM enables to obtain a new volume representation of organ volume models which simultaneously (1) represents by simple primitives the shapes of the whole organ and its internal structures and (2) describes the relationship among the external surface and internal structures of the organ.

Insects are very convenient for studying the scaling of organs and tissues which is associated with extreme miniaturization: first, they have a huge range of body sizes (the largest is more than 2000 times as long as the smallest); second, the smallest insects are comparable in size to unicellular organisms but retain high morphological complexity. Most insect organs display a huge potential for scaling and for retaining their organization and sometimes even their constant relative volume in spite of their size decreasing to only a small fraction of its initial value. By contrast, the relative volume of the reproductive and nervous systems increases by a considerable factor as body size decreases.