Segmenting dendritic trees and corneal nerve fibres is challenging due to their uneven and irregular appearance in the respective image modalities. State-of-the-art approaches use hand-crafted features based on local assumptions that are often violated by tortuous and point-like structures, e.g., straight tubular shape. We propose a novel ridge detector, SCIRD, which is simultaneously rotation, scale and curvature invariant, and relaxes shape assumptions to achieve enhancement of target image structures. Experimental results on three datasets show that our approach outperforms state-of-the-art hand-crafted methods on tortuous and point-like structures, especially when captured at low resolution or limited signal-to-noise ratio and in the pr...