在學習目標檢測的過程中，除了看大神的原作之外，還要學習大神的原始碼，通過原作和原始碼才能更好的學習大神的思想。作為一個新手，在閱讀原始碼的過程是一個倍感煎熬的過程，如果大神的程式碼註釋比較少的話，有的時候為了理解某一個程式碼片段，可能需要花上幾天的時間來理解，這是一個很費時的過程。因此，為了以後更好更快的閱讀大神的原始碼，在這裡對所閱讀過的原始碼做一個總結，將一些檢測方法中通用的方法(如資料增強，單或兩階段中的anchors，nms等)總結一下。

1.anchor產生方法

# coding:utf-8
import numpy as np


def _whctrs(anchor):
    """
    Return width, height, x center, and y center for an anchor (window).
    """

    w = anchor[2] - anchor[0] + 1
    h = anchor[3] - anchor[1] + 1
    x_ctr = anchor[0] + 0.5 * (w - 1)
    y_ctr = anchor[1] + 0.5 * (h - 1)
    return w, h, x_ctr, y_ctr


def _mkanchors(ws, hs, x_ctr, y_ctr):
    """
    Given a vector of widths (ws) and heights (hs) around a center
    (x_ctr, y_ctr), output a set of anchors (windows).
    """

    ws = ws[:, np.newaxis]
    hs = hs[:, np.newaxis]
    anchors = np.hstack((x_ctr - 0.5 * (ws - 1),
                         y_ctr - 0.5 * (hs - 1),
                         x_ctr + 0.5 * (ws - 1),
                         y_ctr + 0.5 * (hs - 1)))
    return anchors


def _ratio_enum(anchor, ratios):
    """
    Enumerate a set of anchors for each aspect ratio wrt an anchor.
    """

    w, h, x_ctr, y_ctr = _whctrs(anchor)
    size = w * h
    size_ratios = size / ratios
    ws = np.round(np.sqrt(size_ratios))
    hs = np.round(ws * ratios)
    anchors = _mkanchors(ws, hs, x_ctr, y_ctr)
    return anchors


def _scale_enum(anchor, scales):
    """
    Enumerate a set of anchors for each scale wrt an anchor.
    """

    w, h, x_ctr, y_ctr = _whctrs(anchor)
    ws = w * scales
    hs = h * scales
    anchors = _mkanchors(ws, hs, x_ctr, y_ctr)
    return anchors

def generate_anchors(base_size=16, ratios=[0.5, 1, 2],
                     scales=2 ** np.arange(3, 6)):
    """
    Generate anchor (reference) windows by enumerating aspect ratios X
    scales wrt a reference (0, 0, 15, 15) window.
    """

    base_anchor = np.array([1, 1, base_size, base_size]) - 1
    ratio_anchors = _ratio_enum(base_anchor, ratios)
    anchors = np.vstack([_scale_enum(ratio_anchors[i, :], scales)
                         for i in range(ratio_anchors.shape[0])])
    return anchors
def generate_anchors_single_pyramid(scales, ratios, shape, feature_stride, anchor_stride):
    """
    scales: 1D array of anchor sizes in pixels. Example: [32, 64, 128]
    ratios: 1D array of anchor ratios of width/height. Example: [0.5, 1, 2]
    shape: [height, width] spatial shape of the feature map over which
            to generate anchors.
    feature_stride: Stride of the feature map relative to the image in pixels.
    anchor_stride: Stride of anchors on the feature map. For example, if the
        value is 2 then generate anchors for every other feature map pixel.
    """
    # Get all combinations of scales and ratios
    scales, ratios = np.meshgrid(np.array(scales), np.array(ratios))
    scales = scales.flatten()
    ratios = ratios.flatten()

    # Enumerate heights and widths from scales and ratios
    heights = scales / np.sqrt(ratios)
    widths = scales * np.sqrt(ratios)

    # Enumerate shifts in feature space
    shifts_y = np.arange(0, shape[0], anchor_stride) * feature_stride
    shifts_x = np.arange(0, shape[1], anchor_stride) * feature_stride
    shifts_x, shifts_y = np.meshgrid(shifts_x, shifts_y)

    # Enumerate combinations of shifts, widths, and heights
    box_widths, box_centers_x = np.meshgrid(widths, shifts_x)
    box_heights, box_centers_y = np.meshgrid(heights, shifts_y)


    box_centers = np.stack(
        [box_centers_x, box_centers_y], axis=2).reshape([-1, 2])
    box_sizes = np.stack([box_widths, box_heights], axis=2).reshape([-1, 2])

    # Convert to corner coordinates (x1, y1, x2, y2)
    boxes = np.concatenate([box_centers - 0.5 * box_sizes,
                            box_centers + 0.5 * box_sizes], axis=1)
    return boxes


def generate_anchors_all_pyramids(scales, ratios, feature_shapes, feature_strides,
                             anchor_stride):
    """Generate anchors at different levels of a feature pyramid. Each scale
    is associated with a level of the pyramid, but each ratio is used in
    all levels of the pyramid.
    Returns:
    anchors: [N, (y1, x1, y2, x2)]. All generated anchors in one array. Sorted
        with the same order of the given scales. So, anchors of scale[0] come
        first, then anchors of scale[1], and so on.
    """
    # Anchors
    # [anchor_count, (y1, x1, y2, x2)]
    anchors = []
    for i in range(len(scales)):
        anchors.append(generate_anchors_single_pyramid(scales[i], ratios, feature_shapes[i],
                                        feature_strides[i], anchor_stride))
    return np.concatenate(anchors, axis=0)

if __name__=='__main__':
    import time
    t1 = time.time()
    a = generate_anchors()
    print(time.time() - t1)
    print(a)
    t2=time.time()
    all=generate_anchors_all_pyramids(scales=[32, 64, 128],ratios=(0.5,1,2),feature_shapes=([16,16],[32,32],[64,64]),feature_strides=[4, 8, 16],anchor_stride=1)
    print(time.time()-t2)
    print(all)
 

IoU計算

# coding:utf-8
import numpy as np

def cal_IOU(bbox1, bbox2):
    """
    calculate the IoU of two bbox
    :param bbox1: array([x1,y1,x2,y2])
    :param bbox2: array([x1,y1,x2,y2])
    :return: iou: float
    """
    x0, y0, width0, height0 = bbox1[0], bbox1[1], bbox1[2] - bbox1[0], bbox1[3] - bbox1[1]
    x1, y1, width1, height1 = bbox2[0], bbox2[1], bbox2[2] - bbox2[0], bbox2[3] - bbox2[1]
    min_x, max_x = np.minimum(x0, x1), np.maximum(bbox1[2], bbox2[2])
    width = width0 + width1 - (max_x - min_x)
    min_y, max_y = np.minimum(y0, y1), np.maximum(bbox1[3], bbox2[3])
    height = height0 + height1 - (max_y - min_y)
    if width <= 0 or height <= 0:  # 沒有交集的兩個邊界框設定為0
        return 0
    inter_area = width * height
    area0 = width0 * height0
    area1 = width1 * height1
    iou = inter_area / (area0 + area1 - inter_area)  # 計算公式，iou=交集/（並集-交集）
    return iou

def convert_xywh_to_x1y1x2y2(center):
    """
    convert center box to bounding box
    :param center: array([center_x,center_y,width,height])
    :return: bbox: array([x1,y1,x2,y2])
    """
    x1y1 = center[:2] - 0.5 * center[2:]
    wh = center[:2] + 0.5 * center[2:]
    return np.concatenate((x1y1, wh))

if __name__ == '__main__':
    bbox1 = np.array([100, 100, 250, 250])
    bbox2 = np.array([100, 100, 250, 250])
    iou = cal_IOU(bbox1, bbox2)
    print(iou)
    center = np.array([100, 100, 80, 80])
    bbox3 = convert_xywh_to_x1y1x2y2(center)
    print(bbox3)
 

NMS演算法

#coding:utf-8

import numpy as np
import matplotlib.pyplot as plt
import matplotlib.patches as patches

def nms(bbox,overlap,top_k=200):
    '''
    計算nms
    :param bbox: array()
    :param overlap: float
    :param top_k: 先選取bbox中得分最高的top_k個
    :return: nms之後的bbox: array()
    '''
    if len(bbox)==0:
        pick=[]
    else:
        x1=bbox[:,0]
        y1=bbox[:,1]
        x2=bbox[:,2]
        y2=bbox[:,3]
        score=bbox[:,4]
        area=(x2-x1)*(y2-y1)
        ind=np.argsort(score)
        ind=ind[-top_k:]
        pick=[]
        while len(ind)>0:
            last=len(ind)-1
            i =ind[last]
            pick.append(i)
            suppress=[last]
            for pos in range(last):
                j=ind[pos]
                xx1=np.maximum(x1[i],x1[j])
                yy1=np.maximum(y1[i],y1[j])
                xx2=np.minimum(x2[i],y2[j])
                yy2=np.minimum(y2[i],y2[j])
                w=xx2-xx1
                h=yy2-yy1
                if w>0 and h>0:
                    ol=w*h/area[i]   #這裡有的是使用iou的計算方式，有的不是使用iou，而是：並集/最大得分的面積，這裡使用的就不是iou的計算方式
                    if ol>overlap:
                        suppress.append(pos)
            ind=np.delete(ind,suppress)
    return bbox[pick,:]

def soft_nms(bbox,overlap,threshold=0.3,method='linear',top_k=200):
    '''
    計算soft-nms的方法
    :param bbox: array()
    :param overlap: float,和nms的含義一樣
    :param threshold: float, 將權重處理之後，將小於此閾值的踢掉
    :param method: string, soft-nms的線性和高斯方法
    :param top_k: 先選取bbox中得分最高的top_k個
    :return: nms之後的bbox: array()
    '''
    if len(bbox)==0:
        pick=[]
    else:
        x1=bbox[:,0]
        y1=bbox[:,1]
        x2=bbox[:,2]
        y2=bbox[:,3]
        score=bbox[:,4]
        area=(x2-x1)*(y2-y1)
        ind=np.argsort(score)
        ind=ind[-top_k:]
        pick=[]
        while len(ind)>0:
            last=len(ind)-1
            i =ind[last]
            pick.append(i)
            suppress=[last]
            for pos in range(last):
                j=ind[pos]
                xx1=np.maximum(x1[i],x1[j])
                yy1=np.maximum(y1[i],y1[j])
                xx2=np.minimum(x2[i],y2[j])
                yy2=np.minimum(y2[i],y2[j])
                w=xx2-xx1
                h=yy2-yy1
                if w>0 and h>0:
                    ov = w * h / area[i]
                    if method=='linear':
                        if ov>overlap:
                            weight=1-ov
                        else:
                            weight=ov
                    elif method=='gaussian':
                        weight=np.exp(-(ov * ov)/0.5)   #0.5表示的是高斯函式中的sigma，預設取0.5
                    else:
                        if ov>overlap:
                            weight=0
                        else:
                            weight=1
                    score[j]=weight*score[j]
                if score[j]<threshold:
                    suppress.append(pos)
            ind=np.delete(ind,suppress)
    return bbox[pick,:]

if __name__=='__main__':
    bbox=np.array([[200,200,400,400,0.99],
                   [220,220,420,420,0.9],
                   [100,100,150,150,0.82],
                   [200,240,400,440,0.5],
                   [150,250,300,400,0.88]])
    overlap=0.7
    # pick=nms(bbox,overlap)
    pick=soft_nms(bbox,overlap)
    fig=plt.figure()
    ax=fig.add_subplot(1,1,1,aspect='equal')
    bbox=bbox/500
    pick=pick/500
    for i in range(bbox.shape[0]):
        rect1=patches.Rectangle(xy=(bbox[i,0],bbox[i,1]),width=bbox[i,2]-bbox[i,0],height=bbox[i,3]-bbox[i,1],edgecolor='r', linewidth=1,fill=False)
        plt.text(x=bbox[i,0],y=bbox[i,1],s='%s'%i,color='b')
        ax.add_patch(rect1)
    for i in range(pick.shape[0]):
        rect2=patches.Rectangle(xy=(pick[i,0],pick[i,1]),width=pick[i,2]-pick[i,0],height=pick[i,3]-pick[i,1],edgecolor='b',linewidth=3,fill=False)
        plt.text(x=pick[i,0],y=pick[i,1],s='%s'%i,color='r',fontsize=20)
        ax.add_patch(rect2)
    plt.show()
 

常見的影象預處理操作

#coding:utf-8

import numpy as np
from PIL import Image,ImageOps, ImageEnhance, PILLOW_VERSION
import collections
import math
import numbers

def _is_pil_image(img):
    return isinstance(img,Image.Image)

def _is_numpy_image(img):
    return isinstance(img, np.ndarray) and (img.ndim in {2, 3})

def _to_numpy(img):
    if not _is_pil_image(img):
        raise TypeError('img is not a Image.Image image')
    img=np.asarray(img)
    return img

def normalize(img,mean,std):
    """Normalize a numpy image with mean and standard deviation.
    Args:
        img（numpy）: numpy image of size (C, H, W) to be normalized.
        mean (sequence): Sequence of means for each channel.
        std (sequence): Sequence of standard deviations for each channely.

    Returns:
        Tensor: Normalized Tensor image.
    """
    if not _is_numpy_image(img):
        raise TypeError('img is not a numpy image')
    for i,m,s in zip(img,mean,std):
        i.sub_(mean).div_(std)
    return img

def resize(img,size,interpolation=Image.BILINEAR):
    """Resize the input PIL Image to the given size.
    Args:
        img (PIL Image): Image to be resized.
        size (sequence or int): Desired output size. If size is a sequence like
            (h, w), the output size will be matched to this. If size is an int,
            the smaller edge of the image will be matched to this number maintaing
            the aspect ratio. i.e, if height > width, then image will be rescaled to
            (size * height / width, size)
        interpolation (int, optional): Desired interpolation. Default is
            ``PIL.Image.BILINEAR``
    Returns:
        PIL Image: Resized image.
    """
    if not _is_pil_image(img):
        raise TypeError('img should be PIL Image.Got {}'.format(type(img)))
    if isinstance(size,int):
        w,h=img.size
        if (w<=h and w==size) or (h<=w and h==size):
            return img
        if w < h:
            ow = size
            oh = int(size * h / w)
            return img.resize((ow, oh), interpolation)
        else:
            oh = size
            ow = int(size * w / h)
            return img.resize((ow, oh), interpolation)
    else:
        return img.resize(size[::-1], interpolation)

def pad(img,padding,fill=0,padding_mode='constant'):
    """Pad the given PIL Image on all sides with speficified padding mode and fill value.
    Args:
        img (PIL Image): Image to be padded.
        padding (int or tuple): Padding on each border. If a single int is provided this
            is used to pad all borders. If tuple of length 2 is provided this is the padding
            on left/right and top/bottom respectively. If a tuple of length 4 is provided
            this is the padding for the left, top, right and bottom borders
            respectively.
        fill: Pixel fill value for constant fill. Default is 0. If a tuple of
            length 3, it is used to fill R, G, B channels respectively.
            This value is only used when the padding_mode is constant
        padding_mode: Type of padding. Should be: constant, edge, reflect or symmetric. Default is constant.
            constant: pads with a constant value, this value is specified with fill
            edge: pads with the last value on the edge of the image
            reflect: pads with reflection of image (without repeating the last value on the edge)
                padding [1, 2, 3, 4] with 2 elements on both sides in reflect mode
                will result in [3, 2, 1, 2, 3, 4, 3, 2]
            symmetric: pads with reflection of image (repeating the last value on the edge)
                padding [1, 2, 3, 4] with 2 elements on both sides in symmetric mode
                will result in [2, 1, 1, 2, 3, 4, 4, 3]
    Returns:
        PIL Image: Padded image.
    """
    assert padding_mode in ['constant', 'edge', 'reflect', 'symmetric'], \
        'Padding mode should be either constant, edge, reflect or symmetric'

    if padding_mode == 'constant':
        return ImageOps.expand(img, border=padding, fill=fill)
    else:
        if isinstance(padding, int):
            pad_left = pad_right = pad_top = pad_bottom = padding
        if isinstance(padding, collections.Sequence) and len(padding) == 2:
            pad_left = pad_right = padding[0]
            pad_top = pad_bottom = padding[1]
        if isinstance(padding, collections.Sequence) and len(padding) == 4:
            pad_left = padding[0]
            pad_top = padding[1]
            pad_right = padding[2]
            pad_bottom = padding[3]

        img = np.asarray(img)
        # RGB image
        if len(img.shape) == 3:
            img = np.pad(img, ((pad_top, pad_bottom), (pad_left, pad_right), (0, 0)), padding_mode)
        # Grayscale image
        if len(img.shape) == 2:
            img = np.pad(img, ((pad_top, pad_bottom), (pad_left, pad_right)), padding_mode)

        return Image.fromarray(img)
def crop(img, i, j, h, w):
    """Crop the given PIL Image.

    Args:
        img (PIL Image): Image to be cropped.
        i: Upper pixel coordinate.
        j: Left pixel coordinate.
        h: Height of the cropped image.
        w: Width of the cropped image.

    Returns:
        PIL Image: Cropped image.
    """
    if not _is_pil_image(img):
        raise TypeError('img should be PIL Image. Got {}'.format(type(img)))

    return img.crop((j, i, j + w, i + h))


def center_crop(img, output_size):
    if isinstance(output_size, numbers.Number):
        output_size = (int(output_size), int(output_size))
    w, h = img.size
    th, tw = output_size
    i = int(round((h - th) / 2.))
    j = int(round((w - tw) / 2.))
    return crop(img, i, j, th, tw)


def resized_crop(img, i, j, h, w, size, interpolation=Image.BILINEAR):
    """Crop the given PIL Image and resize it to desired size.

    Notably used in RandomResizedCrop.

    Args:
        img (PIL Image): Image to be cropped.
        i: Upper pixel coordinate.
        j: Left pixel coordinate.
        h: Height of the cropped image.
        w: Width of the cropped image.
        size (sequence or int): Desired output size. Same semantics as ``scale``.
        interpolation (int, optional): Desired interpolation. Default is
            ``PIL.Image.BILINEAR``.
    Returns:
        PIL Image: Cropped image.
    """
    assert _is_pil_image(img), 'img should be PIL Image'
    img = crop(img, i, j, h, w)
    img = resize(img, size, interpolation)
    return img


def hflip(img):
    """Horizontally flip the given PIL Image.

    Args:
        img (PIL Image): Image to be flipped.

    Returns:
        PIL Image:  Horizontall flipped image.
    """
    if not _is_pil_image(img):
        raise TypeError('img should be PIL Image. Got {}'.format(type(img)))

    return img.transpose(Image.FLIP_LEFT_RIGHT)


def vflip(img):
    """Vertically flip the given PIL Image.

    Args:
        img (PIL Image): Image to be flipped.

    Returns:
        PIL Image:  Vertically flipped image.
    """
    if not _is_pil_image(img):
        raise TypeError('img should be PIL Image. Got {}'.format(type(img)))

    return img.transpose(Image.FLIP_TOP_BOTTOM)


def five_crop(img, size):
    """Crop the given PIL Image into four corners and the central crop.

    .. Note::
        This transform returns a tuple of images and there may be a
        mismatch in the number of inputs and targets your ``Dataset`` returns.

    Args:
       size (sequence or int): Desired output size of the crop. If size is an
           int instead of sequence like (h, w), a square crop (size, size) is
           made.
    Returns:
        tuple: tuple (tl, tr, bl, br, center) corresponding top left,
            top right, bottom left, bottom right and center crop.
    """
    if isinstance(size, numbers.Number):
        size = (int(size), int(size))
    else:
        assert len(size) == 2, "Please provide only two dimensions (h, w) for size."

    w, h = img.size
    crop_h, crop_w = size
    if crop_w > w or crop_h > h:
        raise ValueError("Requested crop size {} is bigger than input size {}".format(size,
                                                                                      (h, w)))
    tl = img.crop((0, 0, crop_w, crop_h))
    tr = img.crop((w - crop_w, 0, w, crop_h))
    bl = img.crop((0, h - crop_h, crop_w, h))
    br = img.crop((w - crop_w, h - crop_h, w, h))
    center = center_crop(img, (crop_h, crop_w))
    return (tl, tr, bl, br, center)


def ten_crop(img, size, vertical_flip=False):
    """Crop the given PIL Image into four corners and the central crop plus the
       flipped version of these (horizontal flipping is used by default).

    .. Note::
        This transform returns a tuple of images and there may be a
        mismatch in the number of inputs and targets your ``Dataset`` returns.

       Args:
           size (sequence or int): Desired output size of the crop. If size is an
               int instead of sequence like (h, w), a square crop (size, size) is
               made.
           vertical_flip (bool): Use vertical flipping instead of horizontal

        Returns:
            tuple: tuple (tl, tr, bl, br, center, tl_flip, tr_flip, bl_flip,
                br_flip, center_flip) corresponding top left, top right,
                bottom left, bottom right and center crop and same for the
                flipped image.
    """
    if isinstance(size, numbers.Number):
        size = (int(size), int(size))
    else:
        assert len(size) == 2, "Please provide only two dimensions (h, w) for size."

    first_five = five_crop(img, size)

    if vertical_flip:
        img = vflip(img)
    else:
        img = hflip(img)

    second_five = five_crop(img, size)
    return first_five + second_five


def adjust_brightness(img, brightness_factor):
    """Adjust brightness of an Image.

    Args:
        img (PIL Image): PIL Image to be adjusted.
        brightness_factor (float):  How much to adjust the brightness. Can be
            any non negative number. 0 gives a black image, 1 gives the
            original image while 2 increases the brightness by a factor of 2.

    Returns:
        PIL Image: Brightness adjusted image.
    """
    if not _is_pil_image(img):
        raise TypeError('img should be PIL Image. Got {}'.format(type(img)))

    enhancer = ImageEnhance.Brightness(img)
    img = enhancer.enhance(brightness_factor)
    return img


def adjust_contrast(img, contrast_factor):
    """Adjust contrast of an Image.

    Args:
        img (PIL Image): PIL Image to be adjusted.
        contrast_factor (float): How much to adjust the contrast. Can be any
            non negative number. 0 gives a solid gray image, 1 gives the
            original image while 2 increases the contrast by a factor of 2.

    Returns:
        PIL Image: Contrast adjusted image.
    """
    if not _is_pil_image(img):
        raise TypeError('img should be PIL Image. Got {}'.format(type(img)))

    enhancer = ImageEnhance.Contrast(img)
    img = enhancer.enhance(contrast_factor)
    return img


def adjust_saturation(img, saturation_factor):
    """Adjust color saturation of an image.

    Args:
        img (PIL Image): PIL Image to be adjusted.
        saturation_factor (float):  How much to adjust the saturation. 0 will
            give a black and white image, 1 will give the original image while
            2 will enhance the saturation by a factor of 2.

    Returns:
        PIL Image: Saturation adjusted image.
    """
    if not _is_pil_image(img):
        raise TypeError('img should be PIL Image. Got {}'.format(type(img)))

    enhancer = ImageEnhance.Color(img)
    img = enhancer.enhance(saturation_factor)
    return img


def adjust_hue(img, hue_factor):
    """Adjust hue of an image.

    The image hue is adjusted by converting the image to HSV and
    cyclically shifting the intensities in the hue channel (H).
    The image is then converted back to original image mode.

    `hue_factor` is the amount of shift in H channel and must be in the
    interval `[-0.5, 0.5]`.

    See https://en.wikipedia.org/wiki/Hue for more details on Hue.

    Args:
        img (PIL Image): PIL Image to be adjusted.
        hue_factor (float):  How much to shift the hue channel. Should be in
            [-0.5, 0.5]. 0.5 and -0.5 give complete reversal of hue channel in
            HSV space in positive and negative direction respectively.
            0 means no shift. Therefore, both -0.5 and 0.5 will give an image
            with complementary colors while 0 gives the original image.

    Returns:
        PIL Image: Hue adjusted image.
    """
    if not(-0.5 <= hue_factor <= 0.5):
        raise ValueError('hue_factor is not in [-0.5, 0.5].'.format(hue_factor))

    if not _is_pil_image(img):
        raise TypeError('img should be PIL Image. Got {}'.format(type(img)))

    input_mode = img.mode
    if input_mode in {'L', '1', 'I', 'F'}:
        return img

    h, s, v = img.convert('HSV').split()

    np_h = np.array(h, dtype=np.uint8)
    # uint8 addition take cares of rotation across boundaries
    with np.errstate(over='ignore'):
        np_h += np.uint8(hue_factor * 255)
    h = Image.fromarray(np_h, 'L')

    img = Image.merge('HSV', (h, s, v)).convert(input_mode)
    return img


def adjust_gamma(img, gamma, gain=1):
    """Perform gamma correction on an image.

    Also known as Power Law Transform. Intensities in RGB mode are adjusted
    based on the following equation:

        I_out = 255 * gain * ((I_in / 255) ** gamma)

    See https://en.wikipedia.org/wiki/Gamma_correction for more details.

    Args:
        img (PIL Image): PIL Image to be adjusted.
        gamma (float): Non negative real number. gamma larger than 1 make the
            shadows darker, while gamma smaller than 1 make dark regions
            lighter.
        gain (float): The constant multiplier.
    """
    if not _is_pil_image(img):
        raise TypeError('img should be PIL Image. Got {}'.format(type(img)))

    if gamma < 0:
        raise ValueError('Gamma should be a non-negative real number')

    input_mode = img.mode
    img = img.convert('RGB')

    gamma_map = [255 * gain * pow(ele / 255., gamma) for ele in range(256)] * 3
    img = img.point(gamma_map)  # use PIL's point-function to accelerate this part

    img = img.convert(input_mode)
    return img


def rotate(img, angle, resample=False, expand=False, center=None):
    """Rotate the image by angle.


    Args:
        img (PIL Image): PIL Image to be rotated.
        angle ({float, int}): In degrees degrees counter clockwise order.
        resample ({PIL.Image.NEAREST, PIL.Image.BILINEAR, PIL.Image.BICUBIC}, optional):
            An optional resampling filter.
            See http://pillow.readthedocs.io/en/3.4.x/handbook/concepts.html#filters
            If omitted, or if the image has mode "1" or "P", it is set to PIL.Image.NEAREST.
        expand (bool, optional): Optional expansion flag.
            If true, expands the output image to make it large enough to hold the entire rotated image.
            If false or omitted, make the output image the same size as the input image.
            Note that the expand flag assumes rotation around the center and no translation.
        center (2-tuple, optional): Optional center of rotation.
            Origin is the upper left corner.
            Default is the center of the image.
    """

    if not _is_pil_image(img):
        raise TypeError('img should be PIL Image. Got {}'.format(type(img)))

    return img.rotate(angle, resample, expand, center)


def _get_inverse_affine_matrix(center, angle, translate, scale, shear):
    # Helper method to compute inverse matrix for affine transformation

    # As it is explained in PIL.Image.rotate
    # We need compute INVERSE of affine transformation matrix: M = T * C * RSS * C^-1
    # where T is translation matrix: [1, 0, tx | 0, 1, ty | 0, 0, 1]
    #       C is translation matrix to keep center: [1, 0, cx | 0, 1, cy | 0, 0, 1]
    #       RSS is rotation with scale and shear matrix
    #       RSS(a, scale, shear) = [ cos(a)*scale    -sin(a + shear)*scale     0]
    #                              [ sin(a)*scale    cos(a + shear)*scale     0]
    #                              [     0                  0          1]
    # Thus, the inverse is M^-1 = C * RSS^-1 * C^-1 * T^-1

    angle = math.radians(angle)
    shear = math.radians(shear)
    scale = 1.0 / scale

    # Inverted rotation matrix with scale and shear
    d = math.cos(angle + shear) * math.cos(angle) + math.sin(angle + shear) * math.sin(angle)
    matrix = [
        math.cos(angle + shear), math.sin(angle + shear), 0,
        -math.sin(angle), math.cos(angle), 0
    ]
    matrix = [scale / d * m for m in matrix]

    # Apply inverse of translation and of center translation: RSS^-1 * C^-1 * T^-1
    matrix[2] += matrix[0] * (-center[0] - translate[0]) + matrix[1] * (-center[1] - translate[1])
    matrix[5] += matrix[3] * (-center[0] - translate[0]) + matrix[4] * (-center[1] - translate[1])

    # Apply center translation: C * RSS^-1 * C^-1 * T^-1
    matrix[2] += center[0]
    matrix[5] += center[1]
    return matrix


def affine(img, angle, translate, scale, shear, resample=0, fillcolor=None):
    """Apply affine transformation on the image keeping image center invariant

    Args:
        img (PIL Image): PIL Image to be rotated.
        angle ({float, int}): rotation angle in degrees between -180 and 180, clockwise direction.
        translate (list or tuple of integers): horizontal and vertical translations (post-rotation translation)
        scale (float): overall scale
        shear (float): shear angle value in degrees between -180 to 180, clockwise direction.
        resample ({PIL.Image.NEAREST, PIL.Image.BILINEAR, PIL.Image.BICUBIC}, optional):
            An optional resampling filter.
            See http://pillow.readthedocs.io/en/3.4.x/handbook/concepts.html#filters
            If omitted, or if the image has mode "1" or "P", it is set to PIL.Image.NEAREST.
        fillcolor (int): Optional fill color for the area outside the transform in the output image. (Pillow>=5.0.0)
    """
    if not _is_pil_image(img):
        raise TypeError('img should be PIL Image. Got {}'.format(type(img)))

    assert isinstance(translate, (tuple, list)) and len(translate) == 2, \
        "Argument translate should be a list or tuple of length 2"

    assert scale > 0.0, "Argument scale should be positive"

    output_size = img.size
    center = (img.size[0] * 0.5 + 0.5, img.size[1] * 0.5 + 0.5)
    matrix = _get_inverse_affine_matrix(center, angle, translate, scale, shear)
    kwargs = {"fillcolor": fillcolor} if PILLOW_VERSION[0] == '5' else {}
    return img.transform(output_size, Image.AFFINE, matrix, resample, **kwargs)


def to_grayscale(img, num_output_channels=1):
    """Convert image to grayscale version of image.

    Args:
        img (PIL Image): Image to be converted to grayscale.

    Returns:
        PIL Image:  Grayscale version of the image.
                    if num_output_channels == 1 : returned image is single channel
                    if num_output_channels == 3 : returned image is 3 channel with r == g == b
    """
    if not _is_pil_image(img):
        raise TypeError('img should be PIL Image. Got {}'.format(type(img)))

    if num_output_channels == 1:
        img = img.convert('L')
    elif num_output_channels == 3:
        img = img.convert('L')
        np_img = np.array(img, dtype=np.uint8)
        np_img = np.dstack([np_img, np_img, np_img])
        img = Image.fromarray(np_img, 'RGB')
    else:
        raise ValueError('num_output_channels should be either 1 or 3')
    return img

# if __name__=='__main__':
#     img=Image.open('1.jpg')
#     img.show()