In this study, a Canny-Cauchy edge detection algorithm is proposed to address the issues of unsatisfactory object contour detection performance, high false detection rate, and high missed detection rate of traditional edge detection methods caused by factors, such as Gaussian noise, salt and pepper noise pollution, and small edge gradient changes. The proposed algorithm is an improved Canny algorithm that performs adaptive median filtering preprocessing on salt and pepper noise images to remove salt and pepper noise while protecting edges from blurring. For designing the filter, the algorithm uses the first derivative of the Cauchy distribution function as the edge detection function and obtains the edge detection filter by sampling the function. Theoretical analysis is conducted on the proposed edge detection function according to the three design criteria of edge detection algorithms, and comparative experiments are conducted with other edge detection algorithms on the BSDS500 dataset. The experimental results show that this algorithm can ensure that the peak signal-to-noise ratio of the processed image is greater than 30 dB and the structural similarity is greater than 0.9 under 20% density salt and pepper noise. In addition, this algorithm has a stronger ability to suppress white noise and respond to real edges than the traditional Canny algorithm. Moreover, regarding the BSDS500 dataset, the proposed algorithm exhibites an increase in F1 score and average accuracy by 7.5% and 10.2%, respectively.