# Image Dehazing and Enhancement Using Principal Component Analysis and Modified Haze Features
## 1 Introduction  
As various digital cameras are introduced in the consumer market with related multimedia services, the enhancement of outdoor hazy images attracts increasing interest. Haze occurs when the reflected light from an object is scattered or absorbed by the particles in the atmosphere and results in visibility degradation. In the case of vehicular systems, cameras should acquire as clean of an image as possible, even in bad weather, including hazy and rainy conditions. Since the haze particles limit the performance of the recognition of other vehicles, pedestrian, and traffic signs, haze removal should be performed in the consumer devices to obtain high-quality images. In addition, hazy images lose color information and contrast because of the haze component. To challenge this problem, various haze removal methods have been proposed in the literature. [PERSON] et al. proposed a haze removal method using the dark channel prior (DCP) which consists of the minimum brightness value among the red (R), green (G), and blue (B) pixels in the local image patch [1]. The DCP plays an important role in estimating the transmission and atmospheric light to remove the haze component. However, [PERSON]'s method exhibits inaccurately estimated atmospheric light, especially in the bright region. Moreover, it is not easy to implement the method in consumer devices because of the high computational complexity in refining the transmission. To solve this problem, [PERSON] et al. proposed a linear model to estimate the depth using the color attenuation prior which represents the relationship between the brightness and saturation components of hazy images [2]. [PERSON] et al. estimated the hazy region by estimating the differences between hue components in the hazy image and its semi-inverse [3]. Learning-based haze removal methods were also proposed using haze-relevant features. [PERSON] et al. proposed a haze estimation method by learning a regression model using random forest [4]. [PERSON]'s method can provide better results than existing methods at the cost of an increasing computational load to extract features in overlapping patches. Deep convolutional neural network-based haze removal methods have also been proposed to estimate more accurate transmission information [5; 6]. However, their performance is also limited since transmission and atmospheric light cannot be learned simultaneously. Recently, [PERSON] et al. proposed a haze removal method based on the assumption that pixels having the same color in the haze region lie on the same line in the RGB color space [7]. Although this method uses a local image formation model to estimate the accurate transmission, it provides an over-dehazed result according to the light condition. [PERSON] et al. defined a haze-line based on the observation that haze-free images can be expressed by a finite number of color values [8]. In hazy images, clustered pixels using k-means in haze-free images are distributed along the haze-lines. In order to estimate an optimal solution, [PERSON] et al. proposed a haze removal method by performing contextual regularization using a bounded constraint and weighted \(l_{1}\)-norm [9]. In addition, [PERSON] et al. estimated haze removal using convex optimization based on the discrete Haar wavelet transform to reduce the computational cost [10]. On the other hand, [PERSON] et al. estimated the optimal atmospheric light based on a new geometry assumption in the RGB vector space [11]. This method assumes that the principal component vectors of all the patches in a haze-free image are through the origin of the RGB vector space. However, since the haze component is added to the patch's principal component vector, it cannot be passed through the origin. For that reason, this method estimates the vector of an atmospheric light using a principal component analysis (PCA) of the image patches.