# A Novel Discriminating and Relative Global Spatial Image Representation with Applications in CBIR
## 5 Discussion
### Invariance to Basic Transformations  
Spatial Pyramid Matching (SPM) [16] is the most notable contribution to incorporate spatial context into the BoVW model. SPM captures the absolute spatial distribution of visual words. However, SPM is sensitive to image transformations such as rotation, flipping and translation. For images that are not well-aligned, SPM may lose its discriminative power. An object may rotate by any angle on the image plane (rotation), it may be flipped horizontally or vertically (flipping), or the object may appear anywhere in an image (translation). The proposed approach is capable of addressing various transformations, by encoding the global relative spatial orientation of visual words. This is achieved by computing the angle between identical visual word pairs with respect to the centroid in image. Figure 20 provides an illustration to better understand our approach.  
Figure 19: Average precision of the proposed RGSIR on visual vocabulary of different sizes using different training test ratios.  
The upper region of Figure 20a-c represents the idea of histograms constructed with SPM [16], while the lower region demonstrates the proposed approach Figure 20d-f. In the figures, we can see Figure 20a,d the original image, Figure 20b,e the image rotated by 90\({}^{\circ}\) and Figure 20c,f the vertically flipped image. The performance of SPM [16] degrades in this case, as the objects occupy different regions in the original and transformed images. In Figure 20a the identical visual words are located in the 3 rd and 4 th regions, in Figure 20b they are found in the 2 nd and 4 th regions, while in Figure 20c they are in the 1 st and 2 nd regions, respectively. Hence the three histogram representations will be different for the same image. In the case of the proposed RGSIR, the same histogram representation will be generated for the original and for the transformed images, as the angle between identical visual words with respect to the centroid remains the same.  
Figure 21 presents a graphical comparison of the average precision for the top 20 retrievals with the concurrent state-of-the-art approaches. [PERSON] et al. [54] propose a Rotation Invariant Bag of Visual Words (RIBoW) approach to encode the spatial information using circular image decomposition in combination with a simple shifting operation using global image descriptors. They report improved performance to existing BoVW approaches. Although SPM [16] encodes the spatial information, it is sensitive to rotation, translation and scale variance of an image. The circular decomposition approach [54] partitions the image into sub-images, and features which are then extracted from each sub-image are used for feature representation. The proposed RGSIR provides 10.4% higher retrieval precision compared to the second best method.  
Experimental results demonstrate the superiority of the proposed approach to the concurrent state-of-the-art approaches. It is important to note here that some approaches incorporate the spatial context prior to the visual vocabulary construction step, while others do so after it [9]. The proposed approach adds this information after the visual vocabulary construction step. In future, we intend to enhance the discriminative power of the proposed approach by extracting rotation-invariant features at the feature extraction step, prior to the construction of the visual vocabulary.  
Figure 20: SPM (**a,b,c**) vs.the proposed approach (**d,e,f**). Here (**a,d**) represent the original images, (**b,e**) the images rotated by 90\({}^{\circ}\), and (**c,f**) vertically flipped images.