Image semantic segmentation of repeating patterns without CNNs

Suppose I have one or multiple tiles consisting of a single pattern (e.g. materials like: wood, concrete, gravel...) that I would like to train my classifier on, and then I'll use the trained classifier to determine to which class each pixel in another image belong.

Below are example of two tiles I would like to train the classifier on:

And let's say I want to segment the image below to identify the pixels belonging to the door and those belonging to the wall. It's just an example, I know this image isn't made of exactly the same patterns as the tiles above:

For this specific problem, is it necessary to use convolutional neural networks? Or is there a way to achieve my goal with a shallow neural network or any other classifier, combined with texture features for example?

I've already implemented a classifier with Scikit-learn which works on tile pixels individually (see code below where training_data is a vector of singletons), but I want instead to train the classifier on texture patterns.

# train classifier
classifier = SGDClassifier()
classifier.fit(training_data, training_target)

# classify given image
test_data = image_gray.flatten().reshape((-1, 1))
predictions = classifier.predict(test_data)
image_classified = predictions.reshape(image_gray.shape)

I was reading this review of recent deep learning methods used for image segmentation and the results seem accurate, but since I've never used any CNN before I feel intimidated by it.

from Image semantic segmentation of repeating patterns without CNNs