I want to take an image that looks like this: 
And make it look more like this:
My thinking being you could look a line of 3 pixels and if the left and right most pixel green then fill in the cinter one, and do the same but with 3 horizontal pixels. run that 3 or 4 time's and that would take care of most of it.
You can use the OpenCV Python library for this kind of operation.
More specifically, you can use morphological transformations, which are available in OpenCV:
Morphological transformations are some simple operations based on the image shape. It is normally performed on binary images. It needs two inputs, one is our original image, second one is called structuring element or kernel which decides the nature of operation. Two basic morphological operators are Erosion and Dilation. Then its variant forms like Opening, Closing, Gradient etc also comes into play. We will see them one-by-one with help of following image
You could use a closing operator, which is:
Closing is reverse of Opening, Dilation followed by Erosion. It is useful in closing small holes inside the foreground objects, or small black points on the object.
The result would look something like this:
And the code would look something like this (you would need to load the image and define a kernel:
import cv2
import numpy as np
img = cv2.imread('<path_to_your_image>',0)
kernel = np.ones((5,5),np.uint8)
closing = cv2.morphologyEx(img, cv2.MORPH_CLOSE, kernel)