This paper provides edge detection analysis on images, which consist of different numbers of details (small, medium and high number of details) and which are compressed by different compression algorithms -JPEG, JPEG2000 and SPIHT. Images from the BSD (Berkeley Segmentation Database) database were used and compressed with different number of bits per pixel. The analysis was performed for five edge detectors: Canny, LoG, Sobel, Prewitt, and Roberts. The fidelity of the detected edges was determined using the objective measures Figure of Merit (FOM), F measure and Performance Ratio (PR), where the reference value was taken from the GroundTruth image. Based on the results presented in the tables, it can be concluded that edge detection behaves differently depending on the number of bits per pixel and applied compression algorithm, as well as, the number of details in the image. Roberts operator has been proven to be the best solution, when it is necessary to perform better edge detection over compressed images with small a number of details, but Canny shows better results for images with a high number of details.