python - 通过线性回归进行 tensorflow 图像分割

Question

之前我构建了一个网络来实现二进制图像分割——前景和背景。我通过两种分类来做到这一点。现在，我想对每个像素进行线性回归，而不是二元分类。

假设 ImageView 中有一个 3D 表面，我想用线性值 10 来分割该表面的精确中间。假设表面的边缘为 5。当然，中间的所有体素均在 5-10 范围内。然后，当体素远离表面时，值迅速降至零。

通过二元分类，我在前景处得到了一张带有 1 的图像，在背景处得到了一张带有 1 的图像——换句话说就是一个分类:) 现在我只想得到一张真实图像值如下...

通过这个线性回归示例，我假设我可以简单地将成本函数更改为最小二乘函数 - cost = tf.square(y - pred)。当然，我会改 rebase 本事实。

但是，当我这样做时，我的预测输出 NaN。我的最后一层是矩阵权重值乘以最终输出的线性和。我想这跟这个有什么关系吧？我无法将其设为 tf.nn.softmax() 函数，因为这会将 0 到 1 之间的值标准化。

所以我相信 cost = tf.square(y - pred) 是问题的根源。接下来我尝试了这个... cost = tf.reduce_sum(tf.square(y - pred)) 但这不起作用。

然后我尝试了这个(推荐 here ) cost = tf.reduce_sum(tf.pow(pred - y, 2))/(2 * batch_size) 但这不起作用.

我应该以不同的方式初始化权重吗？标准化权重？

完整代码如下所示:

import tensorflow as tf
import pdb
import numpy as np
from numpy import genfromtxt
from PIL import Image
from tensorflow.python.ops import rnn, rnn_cell
from tensorflow.contrib.learn.python.learn.datasets.scroll import scroll_data

# Parameters
learning_rate = 0.001
training_iters = 1000000
batch_size = 2
display_step = 1

# Network Parameters
n_input_x = 396 # Input image x-dimension
n_input_y = 396 # Input image y-dimension
n_classes = 1 # Binary classification -- on a surface or not
n_steps = 396
n_hidden = 128
n_output = n_input_y * n_classes

dropout = 0.75 # Dropout, probability to keep units

# tf Graph input
x = tf.placeholder(tf.float32, [None, n_input_x, n_input_y])
y = tf.placeholder(tf.float32, [None, n_input_x * n_input_y], name="ground_truth")
keep_prob = tf.placeholder(tf.float32) #dropout (keep probability)

# Create some wrappers for simplicity
def conv2d(x, W, b, strides=1):
    # Conv2D wrapper, with bias and relu activation
    x = tf.nn.conv2d(x, W, strides=[1, strides, strides, 1], padding='SAME')
    x = tf.nn.bias_add(x, b)
    return tf.nn.relu(x)

def maxpool2d(x, k=2):
    # MaxPool2D wrapper
    return tf.nn.max_pool(x, ksize=[1, k, k, 1], strides=[1, k, k, 1],
                          padding='SAME')

def deconv2d(prev_layer, w, b, output_shape, strides):
    # Deconv layer
    deconv = tf.nn.conv2d_transpose(prev_layer, w, output_shape=output_shape, strides=strides, padding="VALID")
    deconv = tf.nn.bias_add(deconv, b)
    deconv = tf.nn.relu(deconv)
    return deconv

# Create model
def net(x, cnn_weights, cnn_biases, dropout):
    # Reshape input picture
    x = tf.reshape(x, shape=[-1, 396, 396, 1])

    with tf.name_scope("conv1") as scope:
    # Convolution Layer
        conv1 = conv2d(x, cnn_weights['wc1'], cnn_biases['bc1'])
        # Max Pooling (down-sampling)
        #conv1 = tf.nn.local_response_normalization(conv1)
        conv1 = maxpool2d(conv1, k=2)

    # Convolution Layer
    with tf.name_scope("conv2") as scope:
        conv2 = conv2d(conv1, cnn_weights['wc2'], cnn_biases['bc2'])
        # Max Pooling (down-sampling)
        # conv2 = tf.nn.local_response_normalization(conv2)
        conv2 = maxpool2d(conv2, k=2)

    # Convolution Layer
    with tf.name_scope("conv3") as scope:
        conv3 = conv2d(conv2, cnn_weights['wc3'], cnn_biases['bc3'])
        # Max Pooling (down-sampling)
        # conv3 = tf.nn.local_response_normalization(conv3)
        conv3 = maxpool2d(conv3, k=2)


    temp_batch_size = tf.shape(x)[0] #batch_size shape
    with tf.name_scope("deconv1") as scope:
        output_shape = [temp_batch_size, 99, 99, 64]
        strides = [1,2,2,1]
        # conv4 = deconv2d(conv3, weights['wdc1'], biases['bdc1'], output_shape, strides)
        deconv = tf.nn.conv2d_transpose(conv3, cnn_weights['wdc1'], output_shape=output_shape, strides=strides, padding="SAME")
        deconv = tf.nn.bias_add(deconv, cnn_biases['bdc1'])
        conv4 = tf.nn.relu(deconv)

        # conv4 = tf.nn.local_response_normalization(conv4)

    with tf.name_scope("deconv2") as scope:
        output_shape = [temp_batch_size, 198, 198, 32]
        strides = [1,2,2,1]
        conv5 = deconv2d(conv4, cnn_weights['wdc2'], cnn_biases['bdc2'], output_shape, strides)
        # conv5 = tf.nn.local_response_normalization(conv5)

    with tf.name_scope("deconv3") as scope:
        output_shape = [temp_batch_size, 396, 396, 1]
        #this time don't use ReLu -- since output layer
        conv6 = tf.nn.conv2d_transpose(conv5, cnn_weights['wdc3'], output_shape=output_shape, strides=[1,2,2,1], padding="VALID")
        x = tf.nn.bias_add(conv6, cnn_biases['bdc3'])

    # Include dropout
    #conv6 = tf.nn.dropout(conv6, dropout)

    x = tf.reshape(conv6, [-1, n_input_x, n_input_y])

    # Prepare data shape to match `rnn` function requirements
    # Current data input shape: (batch_size, n_steps, n_input)
    # Permuting batch_size and n_steps
    x = tf.transpose(x, [1, 0, 2])
    # Reshaping to (n_steps*batch_size, n_input)

    x = tf.reshape(x, [-1, n_input_x])
    # Split to get a list of 'n_steps' tensors of shape (batch_size, n_hidden)
    # This input shape is required by `rnn` function
    x = tf.split(0, n_steps, x)
    # Define a lstm cell with tensorflow
    lstm_cell = rnn_cell.BasicLSTMCell(n_hidden, forget_bias=1.0, state_is_tuple=True, activation=tf.nn.relu)
    # lstm_cell = rnn_cell.MultiRNNCell([lstm_cell] * 12, state_is_tuple=True)
    # lstm_cell = rnn_cell.DropoutWrapper(lstm_cell, output_keep_prob=0.8)
    outputs, states = rnn.rnn(lstm_cell, x, dtype=tf.float32)
    # Linear activation, using rnn inner loop last output
    # pdb.set_trace()
    output = []
    for i in xrange(396):
        output.append(tf.matmul(outputs[i], lstm_weights[i]) + lstm_biases[i])

    return output


cnn_weights = {
    # 5x5 conv, 1 input, 32 outputs
    'wc1' : tf.Variable(tf.random_normal([5, 5, 1, 32])),
    # 5x5 conv, 32 inputs, 64 outputs
    'wc2' : tf.Variable(tf.random_normal([5, 5, 32, 64])),
    # 5x5 conv, 32 inputs, 64 outputs
    'wc3' : tf.Variable(tf.random_normal([5, 5, 64, 128])),

    'wdc1' : tf.Variable(tf.random_normal([2, 2, 64, 128])),

    'wdc2' : tf.Variable(tf.random_normal([2, 2, 32, 64])),

    'wdc3' : tf.Variable(tf.random_normal([2, 2, 1, 32])),
}

cnn_biases = {
    'bc1': tf.Variable(tf.random_normal([32])),
    'bc2': tf.Variable(tf.random_normal([64])),
    'bc3': tf.Variable(tf.random_normal([128])),
    'bdc1': tf.Variable(tf.random_normal([64])),
    'bdc2': tf.Variable(tf.random_normal([32])),
    'bdc3': tf.Variable(tf.random_normal([1])),
}

lstm_weights = {}
lstm_biases = {}

for i in xrange(396):
    lstm_weights[i] = tf.Variable(tf.random_normal([n_hidden, n_output]))
    lstm_biases[i] = tf.Variable(tf.random_normal([n_output]))


# Construct model
# with tf.name_scope("net") as scope:
pred = net(x, cnn_weights, cnn_biases, keep_prob)
# pdb.set_trace()
pred = tf.pack(pred)
pred = tf.transpose(pred, [1,0,2])
pred = tf.reshape(pred, [-1, n_input_x * n_input_y])

with tf.name_scope("opt") as scope:
    # cost = tf.reduce_sum(tf.square(y-pred))
    cost = tf.reduce_sum(tf.pow((pred-y),2)) / (2*batch_size)
    optimizer = tf.train.AdamOptimizer(learning_rate=learning_rate).minimize(cost)

# Evaluate model
with tf.name_scope("acc") as scope:
    # accuracy is the difference between prediction and ground truth matrices
    correct_pred = tf.equal(0,tf.cast(tf.sub(cost,y), tf.int32))
    accuracy = tf.reduce_mean(tf.cast(correct_pred, tf.float32))

# Initializing the variables
init = tf.initialize_all_variables()
saver = tf.train.Saver()
# Launch the graph
with tf.Session() as sess:
    sess.run(init)
    summary = tf.train.SummaryWriter('/tmp/logdir/', sess.graph) #initialize graph for tensorboard
    step = 1
    # Import data
    data = scroll_data.read_data('/home/kendall/Desktop/')
    # Keep training until reach max iterations
    while step * batch_size < training_iters:
        batch_x, batch_y = data.train.next_batch(batch_size)
        # Run optimization op (backprop)
        # pdb.set_trace()
        batch_x = batch_x.reshape((batch_size, n_input_x, n_input_y))
        batch_y = batch_y.reshape(batch_size, n_input_x * n_input_y)
        sess.run(optimizer, feed_dict={x: batch_x, y: batch_y})
        step = step + 1
        if step % display_step == 0:
            batch_y = batch_y.reshape(batch_size, n_input_x * n_input_y)
            loss, acc = sess.run([cost, accuracy], feed_dict={x: batch_x,
                                                              y: batch_y})


            # Make prediction
            im = Image.open('/home/kendall/Desktop/cropped/temp data0001.tif')
            batch_x = np.array(im)
            batch_x = batch_x.reshape((1, n_input_x, n_input_y))
            batch_x = batch_x.astype(float)
            prediction = sess.run(pred, feed_dict={x: batch_x})
            prediction = prediction.reshape((1, n_input_x * n_input_y))
            prediction = tf.nn.softmax(prediction)
            prediction = prediction.eval()
            prediction = prediction.reshape((n_input_x, n_input_y))

            # my_accuracy = accuracy_custom(temp_arr1,batch_y[0,:,:,0])
            #
            # print "Step = " + str(step) + "  |  Accuracy = " + str(my_accuracy)
            print "Step = " + str(step) + "  |  Accuracy = " + str(acc)

            # csv_file = "CNN-LSTM-reg/CNNLSTMreg-step-" + str(step) + "-accuracy-" + str(my_accuracy) + ".csv"
            csv_file = "CNN-LSTM-reg/CNNLSTMreg-step-" + str(step) + "-accuracy-" + str(acc) + ".csv"
            np.savetxt(csv_file, prediction, delimiter=",")

Answer 1

正如评论中所说，良好的权重初始化是模型成功的关键:

• 太高:模型无法学习并可能产生 NaN 值
• 太低:模型学习速度会非常非常慢，因为梯度太小(参见梯度消失)

TensorFlow 中已经提供了很好的初始化 here (作为贡献)，请随意使用它们。