3.7 Experiments
3.7.1 SPD Manifold
For tests on the SPD manifold, an image is described by a set of RCovDs. More specifically, given a block I(x,y)of sizeW×H, letO = {oi}ri=1, oi ∈ Rd be a set ofr observations
extracted from I(x,y), e.g., oi concatenates intensity values, gradients, filter responses, etc.
for image pixeli. Then, block Ican be represented by thed×dRCovD using Eq. (2.2). For classification, the descriptors (e.g., Log-Euclidean or R-VLAD) are fed to a simple Nearest Neighbor (NN) classifier which clearly shows the benefits of our proposal.
3.7.1.1 Head Pose Classification
We study the problem of head pose (orientation) classification utilizing two datasets, namely Heads Of Coffee break (HOCoffee) and Queen Mary University of London (QMUL) datasets Tosato
4In our experiments, as we have seen slight differences in accuracy values using different pooling methods, we
Figure3.2: Examples of the HOCoffee and the QMUL datasets Tosato et al. [2013].
et al. [2013]. The HOCoffee dataset presents 18,117 low-resolution outdoor images, captured by a head detector for the purpose of automatically detecting social interactions. The QMUL head dataset is composed of 19,292 images, captured in an airport terminal. Images of both datasets are of size50×50pixels and split into a predefined training/test partition. There are 9,522 training and 8,595 test images in the HOCoffee dataset spanning six different classes (orientations): back, front, front-left, front-right, left and right. While for the QMUL dataset, 10,517 images are used for training and the remaining 8,775 images are considered for testing. The images are uniformly partitioned into five classes: back, front, left, right and background. The classification task is quite challenging since the datasets feature non-homogeneous illumi- nation and severe occlusions.
As for image descriptor, similar to Tosato et al. [2013], we used a Difference Of Offset Gaussian (DOOG) filter-bank along color and image gradients for both datasets. More specif- ically, the feature vector assigned to each pixel in the image is
ox,y= h IL(x,y),Ia(x,y),Ib(x,y), q I2 x+Iy2, arctan|Ix| |Iy| ,G1(x,y),G2(x,y),· · · ,G8(x,y) i ,
whereIc(x,y),c∈ {L,a,b}, denotes the CIELab color information at position(x,y),Ixand
Iy are luminance derivatives, andGi(x,y)denotes the response of the i-th DOOG centered at
IL(x,y). Therefore, each local RCovD is onS++13 .
In the first column of Table 3.2, we report the recognition accuracies of all the studied methods for the HOCoffee dataset. Several conclusions can be drawn here. First of all, even the simpleR-BOWGoutperforms the previous state-of-the-art method, demonstrating the ad-
§3.7 Experiments 33
Table3.2: Recognition accuracies in % for the HOCoffee and QMUL datasets Tosato et al. [2013].
Method HOCoffee QMUL
WARCO 80.8 Tosato et al. [2013] 91.2 Tosato et al. [2013]
BOWLE 81.6 87.2 R-BOWG 81.8 87.6 VLADLE 82.4 87.8 R-SCG 83.2 91.7 R-SCS 83.1 91.6 R-SCJ 82.9 91.2 R-LLCG 84.0 92.1 R-LLCS 83.8 91.7 R-LLCJ 83.7 91.5 R-CCG 82.7 90.6 R-CCS 82.6 90.5 R-CCJ 82.4 90.1 R-VLADG 85.0 92.5 R-VLADS 84.9 92.5 R-VLADJ 84.5 92.2 HO-R-VLADG 85.3 92.9 HO-R-VLADS 85.0 92.7 HO-R-VLADJ 84.7 92.5
vantageous of local approaches. Compared to sparse coding techniques, R-VLAD coding with all studied metrics achieve higher performances (with a NN classifier), withHO-R-VLADG
being the overall winner in terms of classification accuracy. However, the performance of R- VLAD with the Stein and Jeffrey is on par or slightly worse than that of the geodesic solution while being at least 27 times faster in coding and 65 times faster (especially for the case of Jeffrey) in the training phase. We also observe that the proposed R-VLAD method is signifi- cantly superior as compared to the Log-Euclidean methods, which suggests that the underlying Riemannian structure is better exploited in R-VLAD.
Among sparse coding family methods, R-LLC using the geodesic distance obtains the highest accuracy. Here, collaborative construction of codes using all codebook atoms as in the variants of R-CC yields slightly inferior recognition accuracy. However, the accuracy numbers are still better than the previous state-of-the-art.
The second column of Table 3.2, reports recognition accuracies of all the studied methods for the QMUL dataset. Similar to the previous experiment, regardless of the metric, the perfor-
mance is improved by considering the higher order information. TheHO-R-VLADGachieves the highest classification accuracy which is nearly 1.7 percentage points greater than Tosato et al. [2013]. Furthermore, theR-VLADSworks on par with theR-VLADGwhile both are the
preferred techniques to theR-VLADJ in terms of classification accuracy. Among the sparse
coding family methods, the highest accuracy is obtained when the geodesic distance is used while sparse coding with the Jeffrey divergence yields the lowest accuracy number.
Moreover, we evaluated the performance of the VLAD in Euclidean space (VLADE) using
very small to large codebook sizes to obtain signatures with the dimensionality similar or greater than that of R-VLAD’s signatures. We observed that R-VLAD is significantly superior toVLADE. For instance, the best accuracy ofVLADEon the HOCoffee and QMUL datasets
are 79.9% and 85.7%, respectively.