Thin plate spline transform gives solid color for certain inputs

首先，使用 test.png 以及报告的 Python 3.13.5 和 OpenCV 4.12.0.88 版本运行提供的 Python 复现程序。比较九点变换和八点变换，然后确定故障所在，并验证九点恒等变换不再生成纯色图像。

Certain combinations of points for a thin plate spline transformation cause the transformed image to be one solid color. Removing the offending combination of points will cause the image to transform as expected.

Below is code that reads the attached image and applys a transformation which should do nothing to the image. The first transformation erroneously turns the whole image a single color. The second transformation uses one less point and correctly does nothing to the image. Im not sure what makes combinations of points not compatible with each other. The points in the code are outside of the uploaded image, since the points were originally being used on a much larger image. I can't upload that here due to file size restrictions. However behavior on the smaller image is the same. Versions are Python 3.13.5, opencv-contrib-python 4.12.0.88, opencv-python 4.12.0.88, Windows 10.

import cv2
import numpy

# Variable initilization
img = cv2.imread('test.png')
base_points = numpy.array([[ 121, 5213],
                    [6197, 5197],
                    [1627, 3481],
                    [3146, 3477],
                    [4668, 3473],
                    [1616, 1752],
                    [4655, 1744],
                    [6179, 1742],
                    [  87,   29]])

# In this example a tps transformation is done.
# The input and output points are the same so the image shouldn't change.
# The whole image will be the color of the one of the corner pixels.
points = base_points[:]
points = points.reshape((-1,points.shape[0],2)).astype(numpy.int32)
tps = cv2.createThinPlateSplineShapeTransformer()
matches = [cv2.DMatch(i, i, 0) for i in range(points.shape[1])]
tps.estimateTransformation(points, points, matches)
warped1 = tps.warpImage(img)
cv2.imshow('Whole image is one color', warped1)

# This example uses one less point.
# The output is the input image, which is what would be expected.
points = base_points[1:]
points = points.reshape((-1,points.shape[0],2)).astype(numpy.int32)
tps = cv2.createThinPlateSplineShapeTransformer()
matches = [cv2.DMatch(i, i, 0) for i in range(points.shape[1])]
tps.estimateTransformation(points, points, matches)
warped2 = tps.warpImage(img)
cv2.imshow('Image is as expected', warped2)

cv2.waitKey(0)

Correct image:

Single color image: