How to crop face regions using convexhull polygons

I am using landmark points from dlib library to select the forehead, nose and eye area from my face based on this question: Is there a way to get the area of the forehead (bounding box) by using opencv/dlib and for a live stream video. It works like a charm and i have the points exactly where i want them, what i would like to do is crop the image where the landmarks are set using convexhull polygons.

What i am trying to do is go from this:

to this:

And save it afterwards

Is there a any way to do it? even if it doesn't look pretty. Here's my current code for facial tracking:

import cv2
import dlib
from imutils import face_utils
import imutils
import numpy as np

cap = cv2.VideoCapture(0)


detector = dlib.get_frontal_face_detector()
predictor = dlib.shape_predictor("shape_predictor_81_face_landmarks.dat")

def face_remap(shape):
    remapped_image = cv2.convexHull(shape)
    return remapped_image


while True:
    _, frame = cap.read()
    gray = cv2.cvtColor(frame, cv2.COLOR_BGR2GRAY)
    out_face = np.zeros_like(frame)
    faces = detector(gray, 1) 

    for face in faces:
        x1 = face.left()
        y1 = face.top()
        x2 = face.right()
        y2 = face.bottom()
        aam = [17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 77, 75, 75, 55, 69, 70, 71, 80, 72, 73, 79, 74, 78]

        landmarks = predictor(gray, face)
        shape = face_utils.shape_to_np(landmarks)
        remapped_shape = np.zeros_like(shape) 
        feature_mask = np.zeros((frame.shape[0], frame.shape[1]))   
        
        x_pts = []
        y_pts = []
        for n in (aam):
            x = landmarks.part(n).x
            y = landmarks.part(n).y

            x_pts.append(x)
            y_pts.append(y)

            cv2.circle(frame, (x, y), 1, (255, 0, 0), -1)
        x1 = min(x_pts)
        x2 = max(x_pts)
        y1 = min(y_pts)
        y2 = max(y_pts)

        cv2.rectangle(frame, (x1, y1), (x2, y2), (0, 0, 255), 3)

    cv2.imshow("out", frame)
    k = cv2.waitKey(1)
    if k == 27:
        remapped_shape = face_remap(shape)
        cv2.fillConvexPoly(feature_mask, remapped_shape[0:27], 1)
        feature_mask = feature_mask.astype(np.bool)
        out_face[feature_mask] = frame[feature_mask]
        cv2.imwrite("out_face.png", out_face)
        break
        

    
cap.release()
cv2.destroyAllWindows()

this code will crop the face image from the background and set the landmark as showed in the example. however i would like to crop around the landmarks

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