## 3 Component-Wise Details of LPaMI
### Recognizing OOIs from Photographs
#### 3.1.2 Feature Extraction  
We select a state-of-the-art approach, gradient local auto-correlations (GLACs) [19], for the feature extraction process in LPaMI. The GLAC descriptor is an efficient method for obtaining shift-invariant features. This technique is considered as an extended form of the histogram of oriented gradients (HOG) [20] and scale-invariant feature transform (SIFT) [13]. It can also be employed as a local feature descriptor. GLACs extract more features since they are second-order statistics of gradients. They are built on the spatial and orientational auto-correlations of image gradients. Below we formally explain our feature extraction process using GLACs.  
Let \(R\) be an image region and \(p\) = (\(x\), \(y\))\(t\) is a position vector. For each pixel, the image gradient \(\left(\frac{\delta R}{\delta x},\frac{\delta R}{\delta y}\right)^{t}\) can be represented as the magnitude \(m=\sqrt{\frac{\delta R^{2}}{\delta x}+\frac{\delta R^{2}}{\delta y}}\) and the orientation angle \(\theta=arctan\left(\frac{\delta R}{\delta x},\frac{\delta R}{\delta y}\right)\). Voting weights to the nearest bins are applied to code the orientation angle \(\theta\) into \(D\) orientation bins. With the gradient orientation vector \(f\) along with the gradient magnitude \(m\), the \(N\)th order auto-correlation function of gradients in local neighbours can be described as  
\[G\left(d_{0},\,...\,d_{N},\,a_{1},\,...,\,a_{N}\right)=\,\,\int w\,\,\left[m \left(p\right),...,m\left(p+a_{N}\right)\right]\,f_{d_{0}}\left(p\right)f_{d_ {1}}\left(p+a_{1}\right)...f_{d_{N}}\left(p+a_{N}\right)dp \tag{1}\]  
Figure 5: (**a**) Proposed method for object of interest (OOI) recognition; (**b**) Spatial auto-correlation patterns of \(\left(p,p+a1\right)\). GLACs: gradient local auto-correlations.  
where \(a_{i}\) represents displacement vectors from the reference point \(p\), \(w\) is a weighting function, and \(f_{d}\) is the \(d\)th element of \(f\). Figure 5b shows spatial auto-correlation patterns. In this study, we consider \(N\in\left\{0,1\right\}\), \(a_{1_{x,y}}\in\left\{\pm\right.\left.\Delta r,\,0\right\}\), and \(w\left(\cdot\right)=min\left(\cdot\right)\) according to [19]. For \(N\in\left\{0,\,1\right\}\), GLACs can be expressed as  
\[0^{th}\;order,\;\;G_{N=0}\left(d_{0}\right)=\;\;\sum_{p\in R}m\left(p\right)f_ {d_{0}}\left(p\right) \tag{2}\]  
\[1^{st}\;order,G_{N=1}\left(d_{0},d_{1},\;a_{1}\right)=\sum_{p\in R}min\left[m \left(p\right),m\left(p+a_{1}\right)\right]f_{d_{0}}\left(p\right)f_{d_{1}} \left(p+a_{1}\right) \tag{3}\]  
```
0: Image collection \(C\) of a given application area obtained from the smartphone of a user \(U\), Number of Trees \(num\)_Trees_, Number of Attributes \(num\)_Attr_, Splitting Node Size \(nodeSize\)
0: Classify the OOI and Extract the Date and Time from \(C\) onto the disk
1: Read images from \(C\) into \(I\)
2: Find Date and Time as image infomation from \(I\)
3: Perform RGB to Gray scaling of \(I\) and save into \(Im_{cov}\)
4: Resize the \(Im_{cov}\) into \(Im_{resize}\)
5: Perform feature extraction using GLACs as \(\left(Im_{resize}\right)\
eg Feature_{vec}\)
6: Compute scores as \(\left[ensemble,scores\right]=ExtraTree(num\)_Trees,numAttr,nodeSize, trainSet,input\)Type)
7: Determine the scene type as \(Category\) via \(predictWith_{ExtraTree}(ensemble,Feature_{vec})\)
8: Write the output in the file \(\left(Category,Date,Time\right)\)
```  
**Algorithm 2** Recognition of Objects of Interest from Photographs