Is there something like class-based object detection? Or class-based selective search? I've been reading a lot about computer vision lately, and while there is a huge amount of info about object classification, and a lot less on object detection, I have not found anything on class-based object detection i.e when I know what I am looking for. For example, looking for cats on a picture. Nowadays you can say if a picture is a cat (object classification), or if the picture has cats among other things. 
How would I use this knowledge to improve the performance (in both accuracy and speed)? 

Somethings that I wouldn't do (but i'm tempted to do):


Perform a brute-force solution with a binary classifier
Implement a shape-based selective search and then use a binary classifier


What i would really like to do, but haven't found in the literacy:


Implement a trainable selective search to find class-based regions of interest. 
Use a binary classifier to check if ROI is in fact the object to be found.
Object detection models (such as SSD, Faster-RCNN, YOLO, R-FCN) are trained to detect specific classes.

If you wish to detect a single class, you could train a custom model on this class.