I'm making my first thing with libgdx. That's a tiled 2D game. Say I have two types of tiles: blue and green. Those are 32x32 pixel images that cover one cell on the game field. I want to be able to create a transition between tiles such as the one on the right of the image attached. Blue and green doesn't mean all pixels in a tile are the same color, that just defines what texture a pixel is from.

I'm not asking about an algorithm — I've already done it via canvas in JavaScript. I just need some directions on what classes/techniques/solutions to use specifically in libgdx.
So I need to take pixels from the blue texture and draw them above the green one. Is there a way to do this with a shader or maybe by directly taking pixel values from blue tile's texture?
Say I already have all my textures (with no transition sprites yet calculated) loaded in a TextureAtlas. What classes should go next to get the desired effect?
Update: Here is a rough example of what my code currently is. My gameScreen.render() method looks simply like this:
batch.begin();
for (int x = 0; x < width; x++) {
for (int y = 0; y < height; y++) {
Sprite sprite = getFloorSpriteByCell(cells[x][y]);
batch.draw(sprite, x * 32, y * 32);
}
}
batch.end();
and in getFloorSpriteByCell() I choose between some of preloaded sprites, that's all, no fancy level editing in a fancy gui-thing.
I don't use tilemaps, I just need to draw some part of a texture above another texture during rendering.

