Compressive sensing application

Theory

Surface-Based Parking Lot Structure

For car-oriented approaches, which tend to capture the texture characteristics of vehicles, seem to provide suitable solutions to handling the occlusion and shadow effects. In contrast, the space-oriented approaches, which were designed to analyze the texture of the image area corresponding to a vacant parking space, can better handle the perspective distortion by adding 3-D scene information. Hence, if we can find a way to benefit from both kinds of approaches, we may achieve robust performance.

In terms of car-oriented approaches, systems usually check the image area, as shown in Figure 1(a), to check the existence of a car. As for the space-oriented approaches, the pixel-based or texture-based feature inside the region of a parking space is used for analysis, as shown in Figure 1(b). In comparison, our approach treats the parking spaces as a set of cubes, as illustrated in Figure 1(c). Each cube is composed of six patches like Figure 1(d). If looking into the details, we may find that the ground plane of a parking space is the ground patch, while a car is made up of patches. Thus, we suggest using surfaces to represent the parking lot structure so that we can benefit from both the car-oriented and space-oriented methods.

For a structural parking lot, we may detect the status of each parking space by observing occlusion patterns inside each image patch. To be specific, we demonstrate various kinds of patterns inside different projection patches in Figure 2. In total, there are 14 different patterns. Here, owing to the regularity of occlusion patterns among objects, an image patch presents distinguishable textures for vacant space detection. Thus, a direct method to determine the parking statuses is to classify the selected patches into one of the 14 occlusion patterns.

Compressive Sensing

Compressed sensing is a signal processing technique for efficiently acquiring and reconstructing a signal, by finding solutions to underdetermined linear systems. This is based on the principle that, through optimization, the sparsity of a signal can be exploited to recover it from far fewer samples than required by the Shannon-Nyquist sampling theorem. There are two conditions under which recovery is possible. The first one is sparsity which requires the signal to be sparse in some domain. The second one is incoherence which is applied through the isometric property which is sufficient for sparse signals. A tutorial on Compressive sensing application for video can be found here.

Compressive Tracking

Tracking algorithms can be generally categorized as either Generative(Generative tracking algorithms typically learn a model to represent the target object and then use it to search for the image region with minimal reconstruction error.) or Discriminative(Discriminative algorithms pose the tracking problem as a binary classification task in order to find the decision boundary for separating the target object from the background.) based on their appearance models.
Compressive Tracking algorithm is an effective and efficient tracking algorithm with an appearance model based on features extracted in the compressed domain. The main components of compressive tracking algorithm are shown by Figure 3.

This appearance model is generative as the object can be well represented based on the features extracted in the compressive domain. It is also discriminative because it uses these features to separate the target from the surrounding background via a naive Bayes classifier. In this appearance model, features are selected by an information-preserving and non-adaptive dimensionality reduction from the multi-scale image feature space based on compressive sensing theories.

Methodology

Results