I prefer region-based computation than pixel wise in this stage. Since K-means is a pixel wise a classification and you need some properties to extract features with certain attributes. So, image-based is better.

Also, you can use hybrid approaches. A sample is existed in my articles and conference papers about automatic building extraction or automatic segmentation. You can refer to my publications.

The answer is problem specific.  pixel-wise If you need a high accuracy, bounding box is easy to handle with fast computing and low accuracy. As trade off, convex hull will be a good choice.

I prefer the region based extracting box counting fractal dimension because of its global approach to investigating the feature

I hope combination is always better ......global features can be extracted region wise which can be complimented with pixel-wise features which lends much more accuracy to the model.......