Sensitivity to image blur

We also tried the robustness on smoothed images, simulating badly focused cameras or image blur. We convolved the original image with the Gaussian kernels of increasing size:

$$I_{blur}(x,y) = I_{orig}(x,y) * G(x,y,\sigma)$$ (5.2)

where $G(x,y,\sigma)$ is defined as:

$$G(x, y, \sigma) = {1 \over 2\pi\sigma^2}e^{-(x^2+y^2)/2\sigma^2}$$

We were increasing $\sigma$ from 0.5 to 3.0 for car images and and from 0.5 to 8.0 for truck images.

Experiment is performed as follows:

• Step 1. Identify learning set $D$ and testing set $T$.
• Step 2. Initialize $\Sigma$ with chosen values: $\Sigma=\{0.5, 1.0, 1.5, 2.0, 2.5, 3.0\}$. Let $\sigma$ is the first member of $\Sigma$;
• Step 3. $T_{\sigma}=\{\}$. For every image $I_{orig}$ in testing set $T$, do a convolution with Gaussian kernel according to the equation 5.2 and construct the new blurred image $I_{blur}$. Add this image $I_{blur}$ to newly created testing set $T_{\sigma}$.
• Step 4. Do the classification with noisyfied testing images $T_{\sigma}$ and learning set $D$.
• Step 5. Let $\sigma$ is the next member of $\Sigma$.
• Step 6. Goto Step 3.
• Step 7. Plot a 2-D graph for every Gaussian kernel size $\sigma$ and corresponding classification rate.