One dimensional edge detection

Question

Instead of edge detection of a 2D image, I would like to detect edges on every single row (i.g. a line) of an image separately. That is detection of edges from an input 1D vector whose values are pixel intensities ranging from 0 to 255 ( image below):

I would like to detect the major edges as appear in the sample input( image below)

Answer 1

One way to get to your desired result is to adapt the 2D Canny edge detector as follows (code in Mathematica):

First, compute the spatial derivative using a Gaussian derivative filter, setting the sigma value relative to the scale of the edges you want to detect. Take the absolute value of the result.

d = Abs@GaussianFilter[data, {{10, 5}}, 1];

Then, determine a threshold automatically to cluster the previous derivative values in two groups (here using Otsu's method).

thrd = FindThreshold[d];

Then, detect the steps of the derivative values (transitions into/from the "dead band").

steps = Flatten@Image`StepDetect[d, thrd]["NonzeroPositions"];

At this point you have the ends of the edges:

ListLinePlot[data, Epilog -> {Red, PointSize[Large], Map[Point[{#, data[[#]]}] &, steps]}]

Optionally--it seems that's what you'd like--keep only the lowest ends of the edges. Clustering the data points at the ends of the edges works in this case, but I'm not sure how robust it is.

t = FindThreshold@data[[steps]];
steps2 = Select[steps, data[[#]] <= t &];

ListLinePlot[data, Epilog -> {Red, PointSize[Large], Map[Point[{#, data[[#]]}] &, steps2]}]