# The Algorithm Framework

Our proposed LLDC method utilizes local distance vector to generate discriminative and effective image features, then adopts coding-pooling framework to obtain robust image representation. To evaluate the effectiveness and generalization of the proposed local distance transformation, we apply two different linear coding method respectively, i.e., LLC [3] and LSC [4], to encode local distance vectors due to their high efficiency and prominent performance.

Within the proposed LLDC framework, the local distance vectors are firstly transformed from local features. Then the local distance vectors and the original local features are separately encoded and pooled to generated two image representations. Finally, we directly concatenate them to extract more discriminative and descriptive image representation while they are complementary to each other.

The overview of the LLDC framework is shown in Fig. 5.2 including following steps:

**Fig. 5.2 ****Overview of the image classification flowchart based on our proposed LLDC method**

- (1) The local features, X = {xi, x
} e M_{2}x_{N}^{DxN}, are extracted from every image; - (2) The local distance vectors, d = {d}N=
_{1}, are transformed from local features one by one following Algorithm 1; - (3) Local distance vectors are encoded by using LSC or LLC coding scheme based on a pre-trained codebook B = {b
_{1;}b_{2},..., b_{M}} e R^{DxM}. The resulted codes are Y = {y_{b}У2,..., Ум*}eR*;^{MxN}

(4) Max-pooling is performed on the codes within each spatial subregion *I ^{i}* as follow:

where max is performed element-wisely for the involved vectors in each subregion and *i =* 1, 2,..., *L* is the numbering of subregions;

(5) The image representation based on local distance vector can be generated by concentrating all the pooled features from every subregion, i.e., V *= *V^{1;} V^{2}’ ...’ *V'f* ]. And the representation is normalized by

- (6) The original local features are also aggregated under the coding-pooling framework through step (3) to (5) to get the image representation
*V*; - (7) The final image representation obtained by combining aforementioned two image representations
*V*and_{d}*V*is fed into a linear SVM classifier for classifying the staining patterns of HEp-2 cells.