Approach of T. Kato, Y. Ninonmiya and I. Masaki [17]

In this paper the multi-clustered modified quadratic discriminant function(MC-MQDF) is used to recognize cars and non-cars images. However the proposed method is capable to learn and classify into various kinds of vehicles: passenger vehicles, commercial vehicles, etc. The MC-MQDF is capable of estimating the complex distribution due to the variety of different possible appearances for preceding vehicles. In a complex distribution test including a variety of vehicles the classification rate for MC-MQDF was approximately 98% while using of the ordinary MQDF resulted in 93% success.

The recognition process can be described as follows:

Learning process.

• Preparation of Training Samples: Vehicle and non-vehicle training samples are extracted from a selection of images in order to provide learning classifiers for vehicle class and non-vehicle class images. The vehicle samples are images cropped by the rectangular windows, which are tangetial to the outlines of vehicle images. The non-vehicle samples are cropped by the rectangular windows which are not tangetial to the outlines of vehicles.
• Feature Extraction: First, the resolutions of all the samples are normalized, since the sizes of the vehicles are not identical to one another. After normalization of the size, all the feature vectors are projected into feature space.
• Learning Classifiers: A classifier is estimated from the distribution of the training samples for each of the classes. Each classifier has a distribution model that containes normal distribution.

Recognition Process.

• Extraction of an image: An image is cropped from a window in an image of a road scene. The window moves around in the image in order to find a vehicle.
• Feature Extraction: Each cropped image is converted to a feature vector, which is the same as in the learning process.
• Classification: Each feature vector is classified as a vehicle or a non-vehicle by the classified from the learning process. If an image is classified as a vehicle, a vehicle must exist at the corresponding window in the road scene.

Feature Extraction Feature extraction was done as follows: all images were normalized to 16x16 image. The feature vector was constructed from the grayscale image using the intensities.

Classification.

In MC-MQDF the clustering starts with the dimension parameter $k=0$, and it is repeated until the goal dimension by increasing $k$ sequentially. For each dimension, the k-means clustering is applied to the training samples with a dynamically changing MQDF metric, which is changed by recomputing of the mean and covariance matrix from the new members of each cluster. The MC-MQDF model estimation procedure can be described as follows.

Step 1. Obtain $n$ initial cluster centroids. (These are chosen at random from training samples in the paper).

Step 2. Start the clutering with the dimension parameter $k=0$.

Step 3. Compute the mean and covariance matrix for each cluster from the corresponding cluster members.

Step 4. Increase the dimension $k$ by an arbitrary step $\Delta k$

Step 5. Re-assign each sample to clusters with the MQDF metric.

Step 6. Re-compute the mean and the covariance matrix for each cluster from its new members.

Step 7. Repeat from Step 5-7 until all cluster members finish changing.

Step 8. If dimension $k$ reaches to goal dimension, the MC-MQDF model estimation is completed. Otherwise return to Step 4.

Database Description.

The database used in this paper had 5000 entries. These images were obtained from videotapes, which were recorded while a vehicle containing an onboard camera drove on highways and on roads in urban areas during daylight hours. The camera was 1/2 CCD monochrome camera with a 16mm-focal length lens, and the captured images consisted of 320x240 pixels with a 256-level gray scale. The evaluation images consist of three types: i) passenger vehicles (sedans, coupes, station wagons and vans); 2) commercial vehicles (buses, trucks, and dump trucks); and 3) motorcycles; In some scenes more then two vehicles were present. The number of motorcycles was very small in comparison to the others. We can see the concept of the proposed method:

Evaluation Method.

In order to reduce the computation time, the evaluations were carried out using test samples consisting of vehicle samples and non-vehicle samples, instead of classifying with a combination of all locations and sizes. Scenes to crop the training samples and the test samples were chosen such that they did not overlap. The training samples for the vehicle were drawn at random from the samples collected. The test samples for the vehicle class were drawn from the remaining images. For the vehicle class, ten training samples were cropped from each vehicle. The test samples were cropped from windows for which approximate locations were given. The training and test samples for the non-vehicle class were cropped at random from the corresponding road scenes, from which the training and test samples for the vehicle were cropped. The sizes of the samples were normalized to 16x16 after cropping the samples from scenes.

Obtained Results.

The maximum classification rate for MC-MQDF for passenger vehicles, commercial vehicles and motorcycles were 99.3%, 97.2%, and 95.6% respectively. The best classification rate for the MC-MQDF was 97.7%.