Finger vein extraction and recognition hold significance in various applications due to the unique and reliable nature of finger vein patterns. While recently finger vein recognition has gained popularity, there are still challenges associated with extracting and processing finger vein patterns related to image quality, positioning and alignment, skin conditions, security concerns and processing techniques applied. In this paper, a method for robust segmentation of line patterns in strongly blurred images is presented and evaluated in vessel network extraction from infrared images of human fingers. In a four-step process: local normalization of brightness, image enhancement, segmentation and cleaning were involved. A novel image enhancement method was used to re-establish the line patterns from the brightness sum of the independent close-form solutions of the adopted optimization criterion derived in small windows. In the proposed method, the computational resources were reduced significantly compared to the solution derived when the whole image was processed. In the enhanced image, where the concave structures have been sufficiently emphasized, accurate detection of line patterns was obtained by local entropy thresholding. Typical segmentation errors appearing in the binary image were removed using morphological dilation with a line structuring element and morphological filtering with a majority filter to eliminate isolated blobs. The proposed method performs accurate detection of the vessel network in human finger infrared images, as the experimental results show, applied both in real and artificial images and can readily be applied in many image enhancement and segmentation applications.