How to set up sass (compass) relative paths?

Question

css

Hello.
gulpfile.js

gulp.task('compass', function() {
  gulp.src(['./app/styles/*.sass', '!app/styles/lib/_*.sass'])
    .pipe(compass({
        css: 'public/css',
        sass: 'app/styles',
        style: 'compact',
        images_dir: 'app/img/', 
        images_path: 'f:/progect/app/img/',
        generated_images_dir: 'public/img/',
        generated_images_path: 'f:/progect/public/img',
    }))
    .pipe(gulp.dest('public/css/'))
    .pipe(connect.reload());
});

Did everything as indicated on the site.
_mixins.sass

$icons: sprite-map("public/img/icons/*.png", $spacing: 10px)

// sized sprites
=image-size($path)
  width: image-width($path)
  height: image-height($path)

=sized-sprite($map, $sprite)
  background: sprite($map, $sprite) no-repeat
  @include image-size(sprite-file($map, $sprite))

=s($sprite, $map: $icons)
  background: sprite($map, $sprite) no-repeat
  //background-image: inline-image('icons/'+$sprite+'.png','image/png'); to switches sprites to base64, elegant
  @include image-size(sprite-file($map, $sprite))

$icons: sprite-map("public/img/icons/*.png", $spacing: 10px)

- That's just with this path, he finds png, regardless of the config. Tried all options. Otherwise it throws an error.
+s(button) - directly insert the mixin itself in the right place to get the effect. After compilation, we get:
url('../img/public/img/icons-s19c8d80a14.png')
But it also generates an image with the following nesting: public/img/public/imj/...png
Despite all this, it works.
To fix nesting we don't need, I change generated_images_path: 'f:/progect/public/', to generated_images_path: 'f:/progect/',
and as a result I get rid of nesting. I put the picture where it needs to be, but here is the relative path:
url('../.../public/img/icons-s19c8d80a14.png')As a result, the browser does not see the picture, because after leaving the styles folder it tries to find the Public folder.

This is for clarity, where and how I have everything located. Help set up such a powerful tool.
How do you set up nesting here, or a relative path to the image? In order not to edit everything by hand, but to give the finished project to work.