Extracting key horizons from seismic images is an important element of the seismic interpretation workflow. Although numerous computer-assisted horizon extraction methods exist, they are typically sensitive to structural and stratigraphic discontinuities. As a result, these computer-assisted methods have difficulties in extracting noncoherent dislocated horizons. We have developed a new data-driven method to correlate, track, and extract horizons from seismic volumes with complex geologic structures. Our method correlates seismic horizons across discontinuities and does not require user input in the form of seed points or prior identification of faults. Furthermore, the method is robust toward amplitude changes along a seismic horizon and does not jump from peak to trough or vice versa. We use a large sliding window and match full-length seismic traces using nonlocal dynamic time warping to extract grids of correlated points for our target horizons. Through computed accuracy measurements, we discard nonaccurate correlations before interpolating complete seismic horizons. Because our method does not require manually picked seed points or prior structural restoration, it does not rely on interpretive experience or geologic knowledge. The proposed method is applied on different real and complex seismic images, with two case examples from the southwestern Barents Sea, and one on the open source Netherlands F3 seismic data.