本文参考Yann LeCun的LeNet5经典架构，稍加ps得到下面适用于本手写识别的cnn结构，构造一个两层卷积神经网络，神经网络的结构如下图所示：

　　输入-卷积-pooling-卷积-pooling-全连接层-Dropout-Softmax输出

　　第一层卷积利用5*5的patch，32个卷积核，可以计算出32个特征。然后进行maxpooling。第二层卷积利用5*5的patch，64个卷积核，可以计算出64个特征。然后进行max pooling。卷积核的个数是我们自己设定，可以增加卷积核数目提高分类精度，但是那样会增加更大参数，提高计算成本。

　　这样输入是分辨率为28*28的图片。利用5*5的patch进行卷积。我们的卷积使用1步长（stride size），0填充模块（zero padded），这样得到的输出和输入是同一个大小。经过第一层卷积之后，卷积特征大小为28*28。然后通过ReLU函数激活。我们的pooling用简单传统的2x2大小的模板做max pooling，这样pooling后得到14*14大小的特征。经过第二层卷积后，卷积特征大小为14*14，然后通过ReLU函数激活，再经过pooling后得到特征大小为7*7。

　　现在，图片尺寸减小到7x7，我们加入一个有1024个神经元的全连接层，用于处理整个图片。我们把池化层输出的张量展开成一些向量，乘上权重矩阵，加上偏置，然后对其使用ReLU。

　　为了避免过拟合，在全连接层输出接上dropout层。Dropout层在训练时屏蔽一半的神经元。

1、输入数据

　　直接使用tensorflow中的模块，导入输入数据：

　　　　from tensorflow.examples.tutorials.mnist import input_data

　　　　mnist = input_data.read_data_sets('MNIST_data', one_hot=True) 

　　或者使用官方提供的input_data.py文件下载mnist数据

2、启动session

　　（1）交互方式启动session

　　　　sess = tf.InteractiveSession()

　　（2）一般方式启动session

　　　　sess = tf.Session()

　　ps: 使用交互方式不用提前构建计算图，而使用一般方式必须提前构建好计算图才能启动session

3、权重和偏置初始化

　　权重初始化的原则：应该加入少量的噪声来打破对称性并且要避免0梯度（初始化为0）

　　权重初始化一般选择均匀分布或是正态分布

　　定义权重初始化方法：

　　　def weight_variable(shape):
　　　　#截尾正态分布,stddev是正态分布的标准偏差
　　　　initial = tf.truncated_normal(shape=shape, stddev=0.1)
　　　　return tf.Variable(initial)

　　定义偏置初始化方法：

　　def bias_variable(shape):
　　　　initial = tf.constant(0.1, shape=shape)
　　　　return tf.Variable(initial)

4、定义卷积和池化方法

　　TensorFlow在卷积和Pooling上有很强的灵活性。我们怎么处理边界？步长应该设多大？在这个实例里，我们的卷积使用1步长（stride size），0填充模块（zero padded），保证输出和输入是同一个大小。我们的pooling用简单传统的2x2大小的模板做maxpooling。为了代码更简洁，我们把这部分抽象成一个函数。

　　def conv2d(x, W):
　　　　return tf.nn.conv2d(x, W, strides=[1, 1, 1, 1],  padding='SAME')
　　def max_pool_2x2(x):
　　　　return tf.nn.max_pool(x, ksize=[1, 2, 2, 1], strides=[1, 2, 2, 1], padding='SAME')

5、直接贴完整代码

from tensorflow.examples.tutorials.mnist import input_data
import tensorflow as tf
#加载数据集
mnist = input_data.read_data_sets('MNIST_data', one_hot=True)

#以交互式方式启动session
#如果不使用交互式session，则在启动session前必须
# 构建整个计算图，才能启动该计算图
sess = tf.InteractiveSession()

"""构建计算图"""
#通过占位符来为输入图像和目标输出类别创建节点
#shape参数是可选的，有了它tensorflow可以自动捕获维度不一致导致的错误
x = tf.placeholder("float", shape=[None, 784]) #原始输入
y_ = tf.placeholder("float", shape=[None, 10]) #目标值

#为了不在建立模型的时候反复做初始化操作，
# 我们定义两个函数用于初始化
def weight_variable(shape):
    #截尾正态分布,stddev是正态分布的标准偏差
    initial = tf.truncated_normal(shape=shape, stddev=0.1)
    return tf.Variable(initial)
def bias_variable(shape):
    initial = tf.constant(0.1, shape=shape)
    return tf.Variable(initial)

#卷积核池化,步长为1,0边距
def conv2d(x, W):
    return tf.nn.conv2d(x, W, strides=[1, 1, 1, 1], padding='SAME')
def max_pool_2x2(x):
    return tf.nn.max_pool(x, ksize=[1, 2, 2, 1],
                          strides=[1, 2, 2, 1], padding='SAME')

"""第一层卷积"""
#由一个卷积和一个最大池化组成。滤波器5x5中算出32个特征，是因为使用32个滤波器进行卷积
#卷积的权重张量形状是[5, 5, 1, 32],1是输入通道的个数，32是输出通道个数
W_conv1 = weight_variable([5, 5, 1, 32])
#每一个输出通道都有一个偏置量
b_conv1 = bias_variable([32])

#位了使用卷积，必须将输入转换成4维向量，2、3维表示图片的宽、高
#最后一维表示图片的颜色通道（因为是灰度图像所以通道数维1，RGB图像通道数为3）
x_image = tf.reshape(x, [-1, 28, 28, 1])

#第一层的卷积结果,使用Relu作为激活函数
h_conv1 = tf.nn.relu(conv2d(x_image, W_conv1))
#第一层卷积后的池化结果
h_pool1 = max_pool_2x2(h_conv1)

"""第二层卷积"""
W_conv2 = weight_variable([5, 5, 32, 64])
b_conv2 = bias_variable([64])
h_conv2 = tf.nn.relu(conv2d(h_pool1, W_conv2) + b_conv2)
h_pool2 = max_pool_2x2(h_conv2)

"""全连接层"""
#图片尺寸减小到7*7，加入一个有1024个神经元的全连接层
W_fc1 = weight_variable([7*7*64, 1024])
b_fc1 = bias_variable([1024])
#将最后的池化层输出张量reshape成一维向量
h_pool2_flat = tf.reshape(h_pool2, [-1, 7*7*64])
#全连接层的输出
h_fc1 = tf.nn.relu(tf.matmul(h_pool2_flat, W_fc1) + b_fc1)

"""使用Dropout减少过拟合"""
#使用placeholder占位符来表示神经元的输出在dropout中保持不变的概率
#在训练的过程中启用dropout，在测试过程中关闭dropout
keep_prob = tf.placeholder("float")
h_fc1_drop = tf.nn.dropout(h_fc1, keep_prob)

"""输出层"""
W_fc2 = weight_variable([1024, 10])
b_fc2 = bias_variable([10])
#模型预测输出
y_conv = tf.nn.softmax(tf.matmul(h_fc1_drop, W_fc2) + b_fc2)

#交叉熵损失
cross_entropy = -tf.reduce_sum(y_ * tf.log(y_conv))

#模型训练,使用AdamOptimizer来做梯度最速下降
train_step = tf.train.AdamOptimizer(1e-4).minimize(cross_entropy)

#正确预测,得到True或False的List
correct_prediction = tf.equal(tf.argmax(y_, 1), tf.argmax(y_conv, 1))
#将布尔值转化成浮点数，取平均值作为精确度
accuracy = tf.reduce_mean(tf.cast(correct_prediction, "float"))

#在session中先初始化变量才能在session中调用
sess.run(tf.initialize_all_variables())

#迭代优化模型
for i in range(20000):
    #每次取50个样本进行训练
    batch = mnist.train.next_batch(50)
    if i%100 == 0:
        train_accuracy = accuracy.eval(feed_dict={
            x: batch[0], y_:batch[1], keep_prob:1.0}) #模型中间不使用dropout
        print("step %d, training accuracy %g" % (i, train_accuracy))
    train_step.run(feed_dict={x:batch[0], y_:batch[1], keep_prob:0.5})
print("test accuracy %g" % accuracy.eval(feed_dict={
            x:mnist.test.images, y_:mnist.test.labels, keep_prob:1.0}))

6、input_data.py文件
　　
注：python3中没有xrange，其range与python2中的xrange作用相同

#!/urs/bin/env python
# -*- coding:utf-8 -*-
# Copyright 2015 Google Inc. All Rights Reserved.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
#     http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
# ==============================================================================
"""Functions for downloading and reading MNIST data."""
from __future__ import absolute_import
from __future__ import division
from __future__ import print_function
import gzip
import os
import tensorflow.python.platform
import numpy
import urllib
import tensorflow as tf

SOURCE_URL = 'http://yann.lecun.com/exdb/mnist/'


def maybe_download(filename, work_directory):
    """Download the data from Yann's website, unless it's already here."""
    if not os.path.exists(work_directory):
        os.mkdir(work_directory)
    filepath = os.path.join(work_directory, filename)
    if not os.path.exists(filepath):
        filepath, _ = urllib.request.urlretrieve(SOURCE_URL + filename, filepath)
        statinfo = os.stat(filepath)
        print('Successfully downloaded', filename, statinfo.st_size, 'bytes.')
    return filepath


def _read32(bytestream):
    dt = numpy.dtype(numpy.uint32).newbyteorder('>')
    return numpy.frombuffer(bytestream.read(4), dtype=dt)[0]


def extract_images(filename):
    """Extract the images into a 4D uint8 numpy array [index, y, x, depth]."""
    print('Extracting', filename)
    with gzip.open(filename) as bytestream:
        magic = _read32(bytestream)
        if magic != 2051:
            raise ValueError(
                'Invalid magic number %d in MNIST image file: %s' %
                (magic, filename))
        num_images = _read32(bytestream)
        rows = _read32(bytestream)
        cols = _read32(bytestream)
        buf = bytestream.read(rows * cols * num_images)
        data = numpy.frombuffer(buf, dtype=numpy.uint8)
        data = data.reshape(num_images, rows, cols, 1)
        return data


def dense_to_one_hot(labels_dense, num_classes=10):
    """Convert class labels from scalars to one-hot vectors."""
    num_labels = labels_dense.shape[0]
    index_offset = numpy.arange(num_labels) * num_classes
    labels_one_hot = numpy.zeros((num_labels, num_classes))
    labels_one_hot.flat[index_offset + labels_dense.ravel()] = 1
    return labels_one_hot


def extract_labels(filename, one_hot=False):
    """Extract the labels into a 1D uint8 numpy array [index]."""
    print('Extracting', filename)
    with gzip.open(filename) as bytestream:
        magic = _read32(bytestream)
        if magic != 2049:
            raise ValueError(
                'Invalid magic number %d in MNIST label file: %s' %
                (magic, filename))
        num_items = _read32(bytestream)
        buf = bytestream.read(num_items)
        labels = numpy.frombuffer(buf, dtype=numpy.uint8)
        if one_hot:
            return dense_to_one_hot(labels)
        return labels


class DataSet(object):
    def __init__(self, images, labels, fake_data=False, one_hot=False,
                 dtype=tf.float32):
        """Construct a DataSet.
        one_hot arg is used only if fake_data is true.  `dtype` can be either
        `uint8` to leave the input as `[0, 255]`, or `float32` to rescale into
        `[0, 1]`.
        """
        dtype = tf.as_dtype(dtype).base_dtype
        if dtype not in (tf.uint8, tf.float32):
            raise TypeError('Invalid image dtype %r, expected uint8 or float32' %
                            dtype)
        if fake_data:
            self._num_examples = 10000
            self.one_hot = one_hot
        else:
            assert images.shape[0] == labels.shape[0], (
                'images.shape: %s labels.shape: %s' % (images.shape,
                                                       labels.shape))
            self._num_examples = images.shape[0]
            # Convert shape from [num examples, rows, columns, depth]
            # to [num examples, rows*columns] (assuming depth == 1)
            assert images.shape[3] == 1
            images = images.reshape(images.shape[0],
                                    images.shape[1] * images.shape[2])
            if dtype == tf.float32:
                # Convert from [0, 255] -> [0.0, 1.0].
                images = images.astype(numpy.float32)
                images = numpy.multiply(images, 1.0 / 255.0)
        self._images = images
        self._labels = labels
        self._epochs_completed = 0
        self._index_in_epoch = 0

    @property
    def images(self):
        return self._images

    @property
    def labels(self):
        return self._labels

    @property
    def num_examples(self):
        return self._num_examples

    @property
    def epochs_completed(self):
        return self._epochs_completed

    def next_batch(self, batch_size, fake_data=False):
        """Return the next `batch_size` examples from this data set."""
        if fake_data:
            fake_image = [1] * 784
            if self.one_hot:
                fake_label = [1] + [0] * 9
            else:
                fake_label = 0
            return [fake_image for _ in range(batch_size)], [
                fake_label for _ in range(batch_size)]
        start = self._index_in_epoch
        self._index_in_epoch += batch_size
        if self._index_in_epoch > self._num_examples:            # Finished epoch            self._epochs_completed += 1            # Shuffle the data            perm = numpy.arange(self._num_examples)            numpy.random.shuffle(perm)            self._images = self._images[perm]            self._labels = self._labels[perm]            # Start next epoch            start = 0            self._index_in_epoch = batch_size            assert batch_size <= self._num_examples        end = self._index_in_epoch        return self._images[start:end], self._labels[start:end]def read_data_sets(train_dir, fake_data=False, one_hot=False, dtype=tf.float32):    class DataSets(object):        pass    data_sets = DataSets()    if fake_data:        def fake():            return DataSet([], [], fake_data=True, one_hot=one_hot, dtype=dtype)        data_sets.train = fake()        data_sets.validation = fake()        data_sets.test = fake()        return data_sets    TRAIN_IMAGES = 'train-images-idx3-ubyte.gz'    TRAIN_LABELS = 'train-labels-idx1-ubyte.gz'    TEST_IMAGES = 't10k-images-idx3-ubyte.gz'    TEST_LABELS = 't10k-labels-idx1-ubyte.gz'    VALIDATION_SIZE = 5000    local_file = maybe_download(TRAIN_IMAGES, train_dir)    train_images = extract_images(local_file)    local_file = maybe_download(TRAIN_LABELS, train_dir)    train_labels = extract_labels(local_file, one_hot=one_hot)    local_file = maybe_download(TEST_IMAGES, train_dir)    test_images = extract_images(local_file)    local_file = maybe_download(TEST_LABELS, train_dir)    test_labels = extract_labels(local_file, one_hot=one_hot)    validation_images = train_images[:VALIDATION_SIZE]    validation_labels = train_labels[:VALIDATION_SIZE]    train_images = train_images[VALIDATION_SIZE:]    train_labels = train_labels[VALIDATION_SIZE:]    data_sets.train = DataSet(train_images, train_labels, dtype=dtype)    data_sets.validation = DataSet(validation_images, validation_labels,                                   dtype=dtype)    data_sets.test = DataSet(test_images, test_labels, dtype=dtype)    return data_sets