Filters and transforms to localize signal transitions

Level transitions in sampled data or digital signals are detected by localizing the zero-crossings of band-pass filtered data. Truncated space-sampled or frequency-sampled representations of the Laplacian-of-Gaussian (LOG) filter in the transform domain and the discrete symmetric cosine transform (DSCT) of the data sequences lead to accurate and robust localization. This paper presents the block-based procedure to adapt the band-pass filter parameter based on estimates of the local gradient. The adaptation leads to reduction in the localization error and increase of the signal-to-noise ratio (SNR) around the transition. The procedure is applied to grayscale images.