Heavy fog degrades the quality of road images in losing contrast and color fidelity, which may cause errors in stereo matching and road segmentation for advanced driver assistance systems (ADAS). Accident rates can be reduced if robust and efficient algorithms are applied for fog removal. Most studies have been conducted on this subject to date, but existing methods are not suitable for heavy haze conditions. Local darkness, under-estimation and over enhancement are always occurred after dehazing. To address these effect this study focuses on video heavy haze removal method by combining dichromatic reflection model with cost function. Our method is based on an observation that fog and highlight share same chromatic properties according to color consistency and physical properties. The dichromatic reflection model can provide an approximate fog map image. A maximum a posteriori formulation is also utilized to robustly refine the fog map and remove black noise. The fog map is used for computing atmospheric light and predicting transmission in order to obtain haze-free images. Experimental results reveal that the proposed method significantly outperforms existing methods in regards to both efficiency and dehazing.