## 2 Methodology
### Segmentation  
Since most scenes are cluttered and contain entities of various shape and form, structured and unstructured, the data is segmented using multiple cues. Instead of seeking consistency along a single cue, which is likely to provide partial results, richer descriptive information is obtained by characterizing entities via a broader set of properties.  
The segmentation makes use of the range data, derived surface normals, and color content as the three individual cues. Its outcome should form a collection of 3D points that must adhere to two conditions: One that segments maintain geometrical connectivity among all points constituting it, and the other is that features of the connected set of points share some degree of similarity. Similarity can be geometrically based, radiometrically based, or both. The transformation of the data into a panorama allows the use of image segmentation procedures for segmenting the point-cloud. We have chosen the use of the mean-shift segmentation [24], due to its successful results with complex and cluttered images. Being non-parametric, it requires neither model parameters nor domain knowledge as inputs. The algorithm is controlled by only two dominant kernel related parameters: the spatial and range dimension size. The first affects the spatial neighborhood while the latter affects the permissible variability within the neighborhood. These two parameters are physical in a sense [24].  
While the mean-shift acts as an instrument to segment the channels, the challenge is to handle the different space partitioning of the individual channels. The aim is to avoid segmentation that either overlays segments or concatenates all features into a feature vector. Such segmentation will be highly dimensional, computationally inefficient, and ultimately yield an over-segmented dataset. Recognizing that the individual channels reflect different data properties and provide optimal segments in some parts, each channel is segmented independently. Then a segmentation that integrates the individual channels is constructed by selecting the significant segments among each. This approach assumes that relevant segments exist in each channel; so, extracting the significant ones from the individual channels can provide a segmentation that features the dominant phenomena in the scene.  
Generally, the objective is to obtain spatially significant and meaningful segments that are uniform in their measured properties. To achieve a spatially significant grouping in object space, a segment score is set as a function of its size in object space. Due to varying scale within a scan, a segment size in image-space (measured by the number of pixels) does not provide a suitable measure. Instead, a 3D coverage, \(r\), is computed via  
\[r=\Delta\varphi\cdot\Delta\theta\sum_{s\in S}\rho_{s}\Rightarrow r\approx \sum_{s\in S}\rho_{s} \tag{3}\]  
where \(\Delta\varphi\), \(\Delta\theta\) are the angular spacing, and \(s\) is the set of pixels relating to segment \(S\).  
Figure 2: Iterative workflow of a multi channel segmentation process.  
The proposed model is applied as follows: first, the largest segment is selected from all channels; if the segment quality is satisfactory, it is inserted into the integrated segmentation. All pixels relating to this segment are then subtracted from all the channels and isolated regions in the other channels are then regrouped and their attribute value is computed. Following, is the extraction of the next largest segment and the repetition of the process until reaching a segment whose size is smaller than a prescribed value and/or preset number of iterations. Figure 2 presents a flowchart diagram of the process. It is noted that due to the non-parametric nature of the mean-shift segmentation, re-segmenting the data between iterations has little effect. We also note that this segmentation can be further refined [25], but results obtained using this approach are sufficient to the present purpose.