这里我只实现功能，具体Android 7.0 的一些细节参考 http://blog.csdn.net/lmj623565791/article/details/72859156

具体步骤：

一、在清单文件中配置provider

<provider
    android:name="android.support.v4.content.FileProvider"
    android:authorities="com.MainActivity.provider"
    android:exported="false"
    android:grantUriPermissions="true">
    <meta-data
        android:name="android.support.FILE_PROVIDER_PATHS"
        android:resource="@xml/file_paths"/>
</provider>

注意：name属性的值是固定的写法，authorities属性的值可以随意写，但是必须要和后面将要说的FileProvider.getUrlForFile()方法中第二个参数一致(我喜欢写包的全路径名)

二、在res目录下创建一个xml文件夹，并创建名为file_paths的xml文件

<?xml version="1.0" encoding="utf-8"?>
<paths>
    <external-path
        name="camera_photos"
        path="" />
</paths>

注意：name属性的值随意写，path属性的值表示共享的具体路径(这里写一个空字符串或.，表示将整个SD卡进行共享)

三、使用下面工具类(包括Fragment中的回调)

/**
 * 相片工具类
 */

public class PhotoUtils {
    private static final String TAG = "PhotoUtils";

    /**
     * @param activity
     *         当前activity
     * @param imageUri
     *         拍照后照片存储路径
     * @param requestCode
     *         调用系统相机请求码
     */
    public static void takePicture(Activity activity, Uri imageUri, int requestCode) {
        //调用系统相机
        Intent intentCamera = new Intent();
        if (Build.VERSION.SDK_INT >= Build.VERSION_CODES.N) {
            intentCamera.addFlags(Intent.FLAG_GRANT_READ_URI_PERMISSION); //添加这一句表示对目标应用临时授权该Uri所代表的文件
        }
        intentCamera.setAction(MediaStore.ACTION_IMAGE_CAPTURE);
        //将拍照结果保存至photo_file的Uri中，不保留在相册中
        intentCamera.putExtra(MediaStore.EXTRA_OUTPUT, imageUri);
        activity.startActivityForResult(intentCamera, requestCode);
    }

    /**
     * @param fragment
     *         当前fragment
     * @param imageUri
     *         拍照后照片存储路径
     * @param requestCode
     *         调用系统相机请求码
     */
    public static void takePicture(Fragment fragment, Uri imageUri, int requestCode) {
        //调用系统相机
        Intent intentCamera = new Intent();
        if (Build.VERSION.SDK_INT >= Build.VERSION_CODES.N) {
            intentCamera.addFlags(Intent.FLAG_GRANT_READ_URI_PERMISSION); //添加这一句表示对目标应用临时授权该Uri所代表的文件
        }
        intentCamera.setAction(MediaStore.ACTION_IMAGE_CAPTURE);
        //将拍照结果保存至photo_file的Uri中，不保留在相册中
        intentCamera.putExtra(MediaStore.EXTRA_OUTPUT, imageUri);
        fragment.startActivityForResult(intentCamera, requestCode);
    }


    /**
     * @param activity
     *         当前activity
     * @param requestCode
     *         打开相册的请求码
     */
    public static void openPic(Activity activity, int requestCode) {
        Intent photoPickerIntent = new Intent(Intent.ACTION_GET_CONTENT);
        photoPickerIntent.setType("image/*");
        activity.startActivityForResult(photoPickerIntent, requestCode);
    }

    /**
     * @param fragment
     *         当前fragment
     * @param requestCode
     *         打开相册的请求码
     */
    public static void openPic(Fragment fragment, int requestCode) {
        Intent photoPickerIntent = new Intent(Intent.ACTION_GET_CONTENT);
        photoPickerIntent.setType("image/*");
        fragment.startActivityForResult(photoPickerIntent, requestCode);
    }

    /**
     * @param activity
     *         当前activity
     * @param orgUri
     *         剪裁原图的Uri
     * @param desUri
     *         剪裁后的图片的Uri
     * @param aspectX
     *         X方向的比例
     * @param aspectY
     *         Y方向的比例
     * @param width
     *         剪裁图片的宽度
     * @param height
     *         剪裁图片高度
     * @param requestCode
     *         剪裁图片的请求码
     */
    public static void cropImageUri(Activity activity, Uri orgUri,
                                    Uri desUri, int aspectX, int aspectY, 
                                    int width, int height, int requestCode) {
        Intent intent = new Intent("com.android.camera.action.CROP");
        if (Build.VERSION.SDK_INT >= Build.VERSION_CODES.N) {
            intent.addFlags(Intent.FLAG_GRANT_READ_URI_PERMISSION);
        }
        intent.setDataAndType(orgUri, "image/*");
        intent.putExtra("crop", "true");
      /*  intent.putExtra("aspectX", aspectX);
        intent.putExtra("aspectY", aspectY);
        intent.putExtra("outputX", width);
        intent.putExtra("outputY", height);*/
        intent.putExtra("scale", true);
        //将剪切的图片保存到目标Uri中
        intent.putExtra(MediaStore.EXTRA_OUTPUT, desUri);
        intent.putExtra("return-data", false);
        intent.putExtra("outputFormat", Bitmap.CompressFormat.JPEG.toString());
        intent.putExtra("noFaceDetection", true);
        activity.startActivityForResult(intent, requestCode);
    }

    /**
     * @param fragment
     *         当前activity
     * @param orgUri
     *         剪裁原图的Uri
     * @param desUri
     *         剪裁后的图片的Uri
     * @param aspectX
     *         X方向的比例
     * @param aspectY
     *         Y方向的比例
     * @param width
     *         剪裁图片的宽度
     * @param height
     *         剪裁图片高度
     * @param requestCode
     *         剪裁图片的请求码
     */
    public static void cropImageUri(Fragment fragment, Uri orgUri, Uri desUri,
                                    int aspectX, int aspectY, int width,
                                    int height, int requestCode) {
        Intent intent = new Intent("com.android.camera.action.CROP");
        if (Build.VERSION.SDK_INT >= Build.VERSION_CODES.N) {
            intent.addFlags(Intent.FLAG_GRANT_READ_URI_PERMISSION);
        }
        intent.setDataAndType(orgUri, "image/*");
        intent.putExtra("crop", "true");
        intent.putExtra("aspectX", aspectX);
        intent.putExtra("aspectY", aspectY);
        intent.putExtra("outputX", width);
        intent.putExtra("outputY", height);
        intent.putExtra("scale", true);
        //将剪切的图片保存到目标Uri中
        intent.putExtra(MediaStore.EXTRA_OUTPUT, desUri);
        intent.putExtra("return-data", false);
        intent.putExtra("outputFormat", Bitmap.CompressFormat.JPEG.toString());
        intent.putExtra("noFaceDetection", true);
        fragment.startActivityForResult(intent, requestCode);
    }

    /**
     * 读取uri所在的图片
     * @param uri
     *         图片对应的Uri
     * @param mContext
     *         上下文对象
     * @return 获取图像的Bitmap
     */
    public static Bitmap getBitmapFromUri(Uri uri, Context mContext) {
        try {
            Bitmap bitmap = MediaStore.Images.Media.
                    getBitmap(mContext.getContentResolver(), uri);
            return bitmap;
        } catch (Exception e) {
            e.printStackTrace();
            return null;
        }
    }

    /**
     * @param context
     *         上下文对象
     * @param uri
     *         当前相册照片的Uri
     * @return 解析后的Uri对应的String
     */
    @SuppressLint("NewApi")
    public static String getPath(final Context context, final Uri uri) {

        final boolean isKitKat = Build.VERSION.SDK_INT >= Build.VERSION_CODES.KITKAT;
        String pathHead = "file:///";
        // DocumentProvider
        if (isKitKat && DocumentsContract.isDocumentUri(context, uri)) {
            // ExternalStorageProvider
            if (isExternalStorageDocument(uri)) {
                final String docId = DocumentsContract.getDocumentId(uri);
                final String[] split = docId.split(":");
                final String type = split[0];
                if ("primary".equalsIgnoreCase(type)) {
                    return pathHead + Environment.getExternalStorageDirectory() + "/" + split[1];
                }
            }
            // DownloadsProvider
            else if (isDownloadsDocument(uri)) {

                final String id = DocumentsContract.getDocumentId(uri);

                final Uri contentUri = ContentUris.
                        withAppendedId(Uri.parse("content://downloads/public_downloads"),
                                Long.valueOf(id));

                return pathHead + getDataColumn(context,
                        contentUri, null, null);
            }
            // MediaProvider
            else if (isMediaDocument(uri)) {
                final String docId = DocumentsContract.getDocumentId(uri);
                final String[] split = docId.split(":");
                final String type = split[0];

                Uri contentUri = null;
                if ("image".equals(type)) {
                    contentUri = MediaStore.Images.Media.EXTERNAL_CONTENT_URI;
                } else if ("video".equals(type)) {
                    contentUri = MediaStore.Video.Media.EXTERNAL_CONTENT_URI;
                } else if ("audio".equals(type)) {
                    contentUri = MediaStore.Audio.Media.EXTERNAL_CONTENT_URI;
                }

                final String selection = "_id=?";
                final String[] selectionArgs = new String[]{split[1]};

                return pathHead + getDataColumn(context, contentUri, selection, selectionArgs);
            }
        }
        // MediaStore (and general)
        else if ("content".equalsIgnoreCase(uri.getScheme())) {
            return pathHead + getDataColumn(context, uri, null, null);
        }
        // File
        else if ("file".equalsIgnoreCase(uri.getScheme())) {
            return pathHead + uri.getPath();
        }
        return null;
    }

    /**
     * Get the value of the data column for this Uri. This is useful for
     * MediaStore Uris, and other file-based ContentProviders.
     * @param context
     *         The context.
     * @param uri
     *         The Uri to query.
     * @param selection
     *         (Optional) Filter used in the query.
     * @param selectionArgs
     *         (Optional) Selection arguments used in the query.
     * @return The value of the _data column, which is typically a file path.
     */
    private static String getDataColumn(Context context, Uri uri,
                                        String selection, String[] selectionArgs) {

        Cursor cursor = null;
        final String column = "_data";
        final String[] projection = {column};
        try {
            cursor = context.getContentResolver().query(uri, projection, selection,
                    selectionArgs, null);
            if (cursor != null && cursor.moveToFirst()) {
                final int column_index = cursor.getColumnIndexOrThrow(column);
                return cursor.getString(column_index);
            }
        } finally {
            if (cursor != null)
                cursor.close();
        }
        return null;
    }

    /**
     * @param uri
     *         The Uri to check.
     * @return Whether the Uri authority is ExternalStorageProvider.
     */
    private static boolean isExternalStorageDocument(Uri uri) {
        return "com.android.externalstorage.documents".equals(uri.getAuthority());
    }

    /**
     * @param uri
     *         The Uri to check.
     * @return Whether the Uri authority is DownloadsProvider.
     */
    private static boolean isDownloadsDocument(Uri uri) {
        return "com.android.providers.downloads.documents".equals(uri.getAuthority());
    }

    /**
     * @param uri
     *         The Uri to check.
     * @return Whether the Uri authority is MediaProvider.
     */
    private static boolean isMediaDocument(Uri uri) {
        return "com.android.providers.media.documents".equals(uri.getAuthority());
    }

}

具体的应用：

public class MainActivity extends AppCompatActivity {
    private ImageView photo;
    private static final int  CODE_GALLERY_REQUEST = 0xa0;
    private static final int  CODE_CAMERA_REQUEST  = 0xa1;
    private static final int  CODE_RESULT_REQUEST  = 0xa2;
    private              File fileUri              = new File(Environment.getExternalStorageDirectory().getPath() + "/photo.jpg");
    private              File fileCropUri          = new File(Environment.getExternalStorageDirectory().getPath() + "/crop_photo.jpg");
    private Uri imageUri;
    private Uri cropImageUri;

    @Override
    protected void onCreate(Bundle savedInstanceState) {
        super.onCreate(savedInstanceState);
        setContentView(R.layout.activity_main);
        photo = (ImageView) findViewById(R.id.iv_photo);
    }

    /**
     * 拍照
     * @param view
     */
    public void takePhoto(View view) {
        if (hasSdcard()) {
            imageUri = Uri.fromFile(fileUri);
            if (Build.VERSION.SDK_INT >= Build.VERSION_CODES.N)
                //通过FileProvider创建一个content类型的Uri
                imageUri = FileProvider.getUriForFile(MainActivity.this, "com.MainActivity.provider", fileUri);
            PhotoUtils.takePicture(MainActivity.this, imageUri, CODE_CAMERA_REQUEST);
        } else {
            Toast.makeText(MainActivity.this, "设备没有SD卡！", Toast.LENGTH_SHORT).show();
            Log.e("asd", "设备没有SD卡");
        }
    }

    /**
     * 调用系统相册
     * @param view
     */
    public void getPhoto(View view) {
        PhotoUtils.openPic(MainActivity.this, CODE_GALLERY_REQUEST);
    }

    @Override
    protected void onActivityResult(int requestCode, int resultCode, Intent data) {
        super.onActivityResult(requestCode, resultCode, data);
        int output_X = 480, output_Y = 480;
        if (resultCode == RESULT_OK) {
            switch (requestCode) {
                case CODE_CAMERA_REQUEST://拍照完成回调
                    cropImageUri = Uri.fromFile(fileCropUri);
                    PhotoUtils.cropImageUri(this, imageUri, cropImageUri, 1, 1, output_X, output_Y, CODE_RESULT_REQUEST);
                    break;
                case CODE_GALLERY_REQUEST://访问相册完成回调
                    if (hasSdcard()) {
                        cropImageUri = Uri.fromFile(fileCropUri);
                        Uri newUri = Uri.parse(PhotoUtils.getPath(this, data.getData()));
                        if (Build.VERSION.SDK_INT >= Build.VERSION_CODES.N)
                            newUri = FileProvider.getUriForFile(this, "com.MainActivity.provider", new File(newUri.getPath()));
                        PhotoUtils.cropImageUri(this, newUri, cropImageUri, 1, 1, output_X, output_Y, CODE_RESULT_REQUEST);
                    } else {
                        Toast.makeText(MainActivity.this, "设备没有SD卡!", Toast.LENGTH_SHORT).show();
                    }
                    break;
                case CODE_RESULT_REQUEST:
                    Bitmap bitmap = PhotoUtils.getBitmapFromUri(cropImageUri, this);
                    if (bitmap != null) {
                        showImages(bitmap);
                    }
                    break;
            }
        }
    }

    /**
     * 展示图片
     * @param bitmap
     */
    private void showImages(Bitmap bitmap) {
        photo.setImageBitmap(bitmap);
    }


    /**
     * 检查设备是否存在SDCard的工具方法
     */
    public static boolean hasSdcard() {
        String state = Environment.getExternalStorageState();
        return state.equals(Environment.MEDIA_MOUNTED);
    }
}

原文