  Scale-invariance, good localization and robustness to noise and distortions
are the main properties that a local feature detector should possess. Most
existing local feature detectors find excessive unstable feature points that
increase the number of keypoints to be matched and the computational time of
the matching step. In this paper, we show that robust and accurate keypoints
exist in the specific scale-space domain. To this end, we first formulate the
superimposition problem into a mathematical model and then derive a closed-form
solution for multiscale analysis. The model is formulated via
difference-of-Gaussian (DoG) kernels in the continuous scale-space domain, and
it is proved that setting the scale-space pyramid's blurring ratio and
smoothness to 2 and 0.627, respectively, facilitates the detection of reliable
keypoints. For the applicability of the proposed model to discrete images, we
discretize it using the undecimated wavelet transform and the cubic spline
function. Theoretically, the complexity of our method is less than 5\% of that
of the popular baseline Scale Invariant Feature Transform (SIFT). Extensive
experimental results show the superiority of the proposed feature detector over
the existing representative hand-crafted and learning-based techniques in
accuracy and computational time. The code and supplementary materials can be
found at~{\url{https://github.com/mogvision/FFD}}.
