Background Subtraction Using Ensembles of Classifiers with an ...

present the color space in Equation 2.15 as another illumination invariant color space. A furtherdiscussion of the observed failures using these alternate color spaces can be found in Section 3.3.l 1 =l 2 =l 3 =(R − G) 2(R − G) 2 + (R − B) 2 + (G − B) 2(R − B) 2(R − G) 2 + (R − B) 2 + (G − B) 2 (2.15)(G − B) 2(R − G) 2 + (R − B) 2 + (G − B) 2Illumination changes often cause errors in background segmentation because when illuminationchanges are sharp the pixel intesity value will vary considerably. When these changes arenot global and isolated in time, careful color space analysis is often used to prevent these illuminationchanges being improperly classified. In [29], Horprasert et al. perform segmentation intofour separate pixel classes: normal background, shaded background, highlighted background, andforeground. This is accomplished by statistically modeling each pixel based on its chromacity κ(Equation 2.18) and brightness α (Equation 2.17), where, over an observed initialization period,µ R (p) is the mean value for the red color channel at pixel p, σ G (p) is the variance over the periodfor the green color channel, and I B (p) is the current value pixel p.α p= argmax α[ (IR (p)−α p·µ R (p)) 2+(IG (p)−α p·µ G (p)σ G (p)σ R (p)()I R (p)·µ R (p)σR 2 + I G (p)·µ G (p)(p)σG 2 + I B (p)·µ B (p)(p)σ([ ] [ ] [ B 2 (p)µR (p) µG (p) µB (p)+ +σ R (p) σ G (p) σ B (p)=) 2 ( ) ]IB (p)−α + p·µ B (p) 2σ B (p)(2.16)]) (2.17)κ p =√ (IR (p)−α p·µ R (p)σ R (p)) 2+(IG (p)−α p·µ G (p)σ G (p)) 2+(IB (p)−α p·µ B (p)σ B (p)) 2(2.18)This model is best understood by considering pixel color values as a vector in a three dimensionalspace, where the red, green and blue color components are the different dimensions. Forany intensity value I(p), changing only the brightness of that color will result in a new intensityI ′ (p), where I ′ (p) = α · I(p). In other words, the new vector I ′ (p) is the same underlying coloras I(p), only its intensity has changed based on the radiance of the pixel under the illuminationcondition. If the chromacity (color) of the pixel has changed to I ′′ (p), however, then κ represents16