# Cost function for image segmentation

I am currently working on image segmentation based on superpixels. My input is a data matrix that contains stixels (rectangular superpixels that span an entire column). In the matrix I have stixel ID, the segment number, the height (in pixels), a label (whether it is an obstacle or ground) and a disparity value obtained from a stereo camera system. I am looking to implement a system as the one described in this paper:

Erbs, Witte, Scharwaechter, Mester, and Franke. Spider-based Stixel object segmentation. Intelligent Vegicles Symposium. (ieeexplore, researchgate)

In that paper they have defined the following cost function: $$p(Z^t|\theta_{map}^t, L^t) \times p(L^{t-1}|Z^t,L^t) \times p(L^t) \times p(\theta_{map}^t|L^t) \times \text{constant}$$ where $t$ is the frame number, $\theta$ is an object parameter vector, $Z$ is a matrix that contains the data of each segment and $L$ is a labeling that assigns each stixel to a specific object. There they infer simultaneously the parameter vector and the label vector. Furthermore they affirm that $L^*$ maximizes $p(L^t|L^{t-1},Z^t)$.

However, they have enough frames that they can use velocity of the objects in addition to the spatial position. Also, they are using the previous labels in their optimization function. I must implement this on single images, so I don't have the information of previous labels or the speed term.

I have tried to adapt their expression under my additional constraints, but I am at a loss when it comes to replacing the temporal dependencies and the labelling dependencies. Would then my $L^*$ depend purely on $Z^t$? And if that is so, how should my optimization function look like?

• So I've been familiarizing myself with MRFs these last couple of days and have come upon what may be a solution. In their work Erbs et al. have enough frames to use motion and from there comes the dependency on time of the labels. However wouldn't it be equivalent (or at least a remedy) to iterate over the same image until a minimum is reached? Also, are there any popular or common potential functions for the cliques used in image segmentation? – RCountZero Oct 21 '15 at 12:52