# Detection of Household Furniture Storage Space in Depth Images
## 3 Methods
### Empty Storage Volume Detection Algorithm
#### 3.1.4 Bounding Box Fine-Tuning
To distinguish the flat histogram from histograms with apparent peaks, the algorithm defines the peak \(H\) as:  
\[H>\tau\cdot\overline{h}\]  
where \(\overline{h}\) is the mean histogram frequency and \(\tau\) is an empirically determined threshold factor. However, finding the peak of each histogram alone does not necessarily correspond to finding the furniture structure that encloses the observed empty storage volume. There are three main cases where this is not possible:  
Figure 6: The detected bounding box is depicted with an orange rectangle. Dilating or contracting that bounding box by \(d_{v}\) would create green or blue bounding boxes, respectively. The highlighted volume between the blue and green bounding boxes contains mesh vertices that enclose the observed storage volume: (**a**) Front view, (**b**) Side view. Figure 7: Mesh vertices distribution in storage volume range along: (**a**) \(z\)-axis (front view), (**b**) \(y\)-axis (front view), (**c**) \(x\)-axis (side view). the histogram is empty;
2. there are no distinguishable peaks in the histogram;
3. there are several peaks in the histogram. The first case occurs when the considered empty storage volume is not completely enclosed by the furniture structure. In this case, the storage volume has no furniture structure above. That is, the storage volume is located on top of the furniture. An example is the table shown in Figure 7(a). In this case, the algorithm uses the height of the detected bounding box as the height of the enclosed bounding box. The histogram has no distinguishable peaks if the axis for which the histogram was calculated is aligned with a storage surface that is not bounded with furniture side-walls in the storage volume range; e.g., Figure 6(a),c. The left-hand histogram in Figure 6(a) shows the histogram calculated in the direction aligned with a storage surface without furniture side-walls that is completely contained in the storage volume range. Figure 6(c) shows an example of a storage volume range that includes empty space and only part of the storage surface without furniture side-walls in the observed direction. It can be noted that the histograms have approximately uniform distribution of the mesh vertices along the supporting surface, and some histogram bins are empty. In both examples the algorithm will choose last non-empty histogram bin to adjust the size of the enclosed storage volume. Multiple peaks in the histogram emerge when the storage volume is enclosed by furniture walls whose thickness is less than the histogram range. Two examples are the right histogram in Figure 6(a) and the bottom histogram in Figure 6(b). In that case, the algorithm chooses the histogram peak that is closer to the center of the observed storage volume. Finally, with the adjusted extents, the algorithm computes the axis-aligned bounding box as the last step in the process of empty storage volume ground truth annotation, which can be used for synthetic scene generation, explained in the next subsection. The considered example of bookshelf model with annotated enclosed storage volumes is shown in Figure 7(c).