How to handle variable sized input in CNN with Keras?

I am trying to perform the usual classification on the MNIST database but with randomly cropped digits. Images are cropped the following way : removed randomly first/last and/or row/column.

I would like to use a Convolutional Neural Network using Keras (and Tensorflow backend) to perform convolution and then the usual classification.

Inputs are of variable size and i can't manage to get it to work.

Here is how I cropped digits

import numpy as np
from keras.utils import to_categorical
from sklearn.datasets import load_digits

digits = load_digits()

X = digits.images
X = np.expand_dims(X, axis=3)

X_crop = list()
for index in range(len(X)):
    X_crop.append(X[index, np.random.randint(0,2):np.random.randint(7,9), np.random.randint(0,2):np.random.randint(7,9), :])
X_crop = np.array(X_crop)

y = to_categorical(digits.target)

from sklearn.model_selection import train_test_split

X_train, X_test, y_train, y_test = train_test_split(X_crop, y, train_size=0.8, test_size=0.2)

And here is the architecture of the model I want to use

from keras.layers import Dense, Dropout
from keras.layers.convolutional import Conv2D
from keras.models import Sequential

model = Sequential()

model.add(Conv2D(filters=10, 
                 kernel_size=(3,3), 
                 input_shape=(None, None, 1), 
                 data_format='channels_last'))

model.add(Dense(128, activation='relu'))
model.add(Dropout(0.2))

model.add(Dense(10, activation='softmax'))


model.compile(loss='categorical_crossentropy', optimizer='sgd', metrics=['accuracy'])

model.summary()

model.fit(X_train, y_train, epochs=100, batch_size=16, validation_data=(X_test, y_test))

1. Does someone have an idea on how to handle variable sized input in my neural network?

2. And how to perform classification?