In this paper, we show that a color image model we recently proposed explains the existence of color lines and predicts that they will have a slope of one. We present experimental results verifying this on several image datasets by showing that images segmented into blocks are often well-described by lines of slope one, that pixels with similar local averages fall on a line of slope one, and that, when all the pixels are normalized to have a local average of zero, they all fall on a line of slope one. We also discuss the image formation models that lead to this prediction and address some of the difficulties previously encountered in using image formation models to explain color lines.
In this paper we incorporate an active contours energy into the Marked Point Process (MPP) framework. The addition of this energy allows the MPP model to detect objects with irregular shapes. This energy accounts for the elasticity and curvature properties of the detected objects. We employ the balloon method to prevent the contour from stagnating at local minima. We use calculus of variations to evolve each individual contour and we use stochastic multiple birth and death dynamics to optimize the MPP energy function. We demonstrate that our method successfully models components with irregular shape in material images, but the model can be extended to other applications.