In the eld of image-guided liver surgery (IGLS), the initial registration of the intra-operative organ surface with preoperative tomographic image data is performed on manually selected anatomical landmarks. In this paper, we introduce a fully automatic scheme that is able to estimate the transformation for initial organ registration in a multi-modal setup aligning intra-operative time-of- ight (ToF) with preoperative computed tomography (CT) data, without manual interaction. The method consists of three stages: First, we extract geometric features that encode the local surface topology in a discriminative manner based on a novel gradient operator. Second, based on these features, point correspondences are established and deployed for estimating a coarse initial transformation. Third, we apply a conventional iterative closest point (ICP) algorithm to re ne the alignment. The proposed method was evaluated for an open abdominal hepatic surgery scenario with invitro experiments on four porcine livers. The method achieved a mean distance of 4.82 0.79 mm and 1.70 0.36 mm for the coarse and ne registration, respectively.
Image-guided surgery techniques augment the anatomical expertise of the
surgeon with a patient-specific source of information by correlating the operative
field with preoperative tomographic image data. This allows the physician to
see the surgical probe position in relation to anatomical structures during the
procedure. Benefits of the integration of computer navigated tool guidance for
hepatic surgery are (i) the enhancement of the resection of subsurface targets and
avoidance of critical structures, (ii) improved outcomes due to reduced resection
margins, and (iii) an expansion of the spectrum of resectability [
The proposed registration framework is composed of three stages (Fig. 1). First, ToF and CT data are preprocessed and transformed into a surface mesh representation. Second, we extract local surface feature descriptors from both data sets. Third, in order to register the surfaces, point correspondences are established by feature matching and a rigid body transformation is estimated. This coarse registration can then be refined with conventional ICP variants. 2.1
ToF imaging directly acquires metric 3D surface information in real-time with a single sensor based on the phase shift between an actively emitted and the reflected optical signal. The measurements of the ToF camera can be represented as a set of points or vertices V = {vi}, i ∈ {1, . . . , w · h}, where vi ∈ R3 denotes the vertex coordinates, w ×h the sensor resolution. In consideration of the inherent noise in ToF range measurements and w.r.t. the trade-off between data denoising and preservation of topological structure, we perform data preprocessing in a way that gives priority to the topological reliability of the surface. In particular, we combine temporal averaging with edge-preserving median and bilateral filtering. In terms of segmentation, for the in-vitro experiments (Sect. 2.5), we used a semi-automatic scheme. The organ is extracted by thresholding and ToF Data
CT Data Registration Refinement (ICP)
Denoising Segmentation
Initial Transformation
Estimation
Segmentation
Mesh
Generation Correspondence
Search
ToF Mesh
CT Mesh CT Descriptors ToF Descriptors
Feature Extraction the remaining point cloud triangulated, providing the intra-operative ToF surface mesh. The anatomical reference surface is segmented from preoperative CT data using a region growing framework with manual seed point placement. Subsequently, we apply the marching cubes algorithm on the extracted binary volumetric segmentation mask and eventually decimate the dense CT mesh. 2.2
In this section, we introduce a gradient operator that computes a numerical
differentiation of a geometric scalar field defined on a 2D manifold. Then, we
present descriptors that encode the spatial distribution and orientation of the
resulting gradient vector field within the local neighborhood of a mesh vertex.
Geometric CUSS Gradient Conventionally, in a 2D image, gradients are
computed by differentiating scalar data in two orthogonal directions. For 2D
manifolds, we propose a novel gradient operator ∇f (vi) that is based on a
circular uniform surface sampling (CUSS) technique being invariant to mesh
representation and density [
P = {ps | ps = vi + rs · Rϕs ai} Finally, the surface sampling is performed by intersecting the mesh with rays that emerge from the points ps and are directed parallel to ni (Fig. 2(a)). The intersection points are denoted ms, the scalar field value f (ms) is interpolated w.r.t. the adjacent vertices. The CUSS gradient ∇f (vi) at the vertex vi can then be expressed as ∇f (vi) = 1
∑Ns f (ms) − f (vi) Ns s=1 ||ms − vi||2 · Rϕs ai (1) (2) 2.3
For each vertex vi, the descriptor extracts the spatial distribution and
orientation of the CUSS gradient vector field (Fig. 2(b)) for the local set of vertices
Vˆ ⊂ V that reside within a spherical volume of interest. First, the gradient
vectors ∇f (vi) are projected onto the three planes of a local coordinate
system. It is spanned by the vertex normal ni and a second axis mi ∈ Ti pointing
into the dominant gradient direction. Second, for each plane, the projected
vectors are separated into circular segments and binned in polar histograms [
For the registration of ToF and CT data (V1,V2), the corresponding sets of local
descriptors D1,D2 are computed first. Based on these descriptor sets, point
correspondences are established between V1 and V2 by searching the mutual
best match with an Euclidean similarity metric. In order to eliminate false
correspondences, the set of point pairs is decimated by comparing all internal
pairwise distances of the two correspondence point sets [
The proposed method was evaluated with in-vitro experiments on four porcine livers. ToF data were acquired with a CamCube 2.0 (PMDTechnologies GmbH) at a distance of 60 cm. CT data were acquired with an Artis zeego C-arm system (Siemens AG, Healthcare Sector). The livers were scanned with a resolution of 512 × 512 × 348 voxels and a spacing of 0.70 × 0.70 × 0.70 mm. 3
Quantitative ToF/CT registration results of the four porcine livers are given in Fig. 3. In order to evaluate the registration accuracy, we measured the residual mean distance d of all ToF surface points to the closest CT surface points. (a) (b) (c) dinit [mm] The proposed method achieved a mean distance between the ToF/CT mesh of dinit = 4.82 ± 0.79 mm for the initial coarse registration and d ne = 1.70 ± 0.36 mm for the subsequent ICP refinement. The descriptor parameters were set heuristically. Qualitative registration results for liver L2 are shown in Fig. 3. The runtime of the intra-operative pipeline (preprocessing, feature extraction, correspondence search, registration) is less than 30 s on a 2.66 GHz CPU, with the correspondence search running on a NVIDIA Geforce 8400 GPU. CT data preprocessing can be performed pre-operatively. 4
We have presented a multi-modal rigid registration framework for estimating the initial alignment of an exposed intra-operative organ surface with preoperative data based on local surface descriptors. Preliminary experimental results on porcine liver data are encouraging and suggest that a feature-based correspondence search can replace the manual selection of anatomical landmarks for ICP initialization in organ registration applications (e.g. IGLS). Ongoing work analyzes the influence of the ToF preprocessing pipeline and the robustness of the descriptor w.r.t. minor deformations.