Gaussian filter for a one dimensional array

Question

I want to apply a 1D Gaussian filter on a 1D array. For Python there are many libraries for this, but i did not find any for android. So i want to do it without a library. What is the best way to do this? Which is the right formula to do this? I found only formulas for 2D spaces

Answer 1

Have you seen this article? It is a JavaScript implementation but should be adaptable to Java.

One-dimensional blur can be computed even faster. E. g. we want to compute horizontal blur. We compute bh[i,j],bh[i,j+1],bh[i,j+2],.... But the neighboring values bh[i,j] and bh[i,j+1] are almost the same. The only difference is in one left-most value and one right-most value. So bh[i,j+1]=bh[i,j]+f[i,j+r+1]−f[i,j−r].

In our new algorithm, we will compute the one-dimensional blur by creating the accumulator. First, we put the value of left-most cell into it. Then we will compute next values just by editing the previous value in constant time. This 1D blur has the complexity O(n) (independent on r). But it is performed twice to get box blur, which is performed 3 times to get gaussian blur. So the complexity of this gaussian blur is 6 * O(n).

function gaussBlur_4 (scl, tcl, w, h, r) {
    var bxs = boxesForGauss(r, 3);
    boxBlur_4 (scl, tcl, w, h, (bxs[0]-1)/2);
    boxBlur_4 (tcl, scl, w, h, (bxs[1]-1)/2);
    boxBlur_4 (scl, tcl, w, h, (bxs[2]-1)/2);
}
function boxBlur_4 (scl, tcl, w, h, r) {
    for(var i=0; i<scl.length; i++) tcl[i] = scl[i];
    boxBlurH_4(tcl, scl, w, h, r);
    boxBlurT_4(scl, tcl, w, h, r);
}
function boxBlurH_4 (scl, tcl, w, h, r) {
    var iarr = 1 / (r+r+1);
    for(var i=0; i<h; i++) {
        var ti = i*w, li = ti, ri = ti+r;
        var fv = scl[ti], lv = scl[ti+w-1], val = (r+1)*fv;
        for(var j=0; j<r; j++) val += scl[ti+j];
        for(var j=0  ; j<=r ; j++) { val += scl[ri++] - fv       ;   tcl[ti++] = Math.round(val*iarr); }
        for(var j=r+1; j<w-r; j++) { val += scl[ri++] - scl[li++];   tcl[ti++] = Math.round(val*iarr); }
        for(var j=w-r; j<w  ; j++) { val += lv        - scl[li++];   tcl[ti++] = Math.round(val*iarr); }
    }
}
function boxBlurT_4 (scl, tcl, w, h, r) {
    var iarr = 1 / (r+r+1);
    for(var i=0; i<w; i++) {
        var ti = i, li = ti, ri = ti+r*w;
        var fv = scl[ti], lv = scl[ti+w*(h-1)], val = (r+1)*fv;
        for(var j=0; j<r; j++) val += scl[ti+j*w];
        for(var j=0  ; j<=r ; j++) { val += scl[ri] - fv     ;  tcl[ti] = Math.round(val*iarr);  ri+=w; ti+=w; }
        for(var j=r+1; j<h-r; j++) { val += scl[ri] - scl[li];  tcl[ti] = Math.round(val*iarr);  li+=w; ri+=w; ti+=w; }
        for(var j=h-r; j<h  ; j++) { val += lv      - scl[li];  tcl[ti] = Math.round(val*iarr);  li+=w; ti+=w; }
    }
}

Answer 2

How about using OpenCV in Android. There are books and articles dedicated to this topic. e.g.

Gaussian Low-pass Filter in Android OpenCV.