How does scale factor behave in HOG multiscale detector ?

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Actually it does exactly the same as any other multiscale detection approach out there. It is used to create the image scale pyramid for multi scale detection using a single scale model.

It takes the following steps

1. Start from a new test image, go with a sliding window approach (where window is model size) through the image and store all detections.
2. Then downscale the image according to the scale factor, where 1.10 means you dowscale both dimensions (rows and cols) with 10%.
3. Again perform detections.
4. Warp the image detections back to the original size of the image using the downscale factor.
5. Do this until one of the dimensions of the image reaches the largest model dimension (because then sliding window is no longer possible).
6. Merge detections on similar locations over different scales.