给定一个输入矩阵，矩阵中包含了多个矩形，这些矩形可能会以奇异的角度排列。我们的目标是从矩阵中提取出矩形并测量其宽度和高度。然而，由于输入矩阵的分辨率较低，因此可能有重叠现象，这会给提取和测量矩形带来困难。
2、解决方案 为了提取和测量矩阵中的矩形，我们可以采用以下步骤：
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收集转换点：首先，我们将矩阵中的所有转换点收集起来。转换点是指从 1 到 0 或从 0 到 1 的变化点。
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计算长度和宽度：接下来，我们可以直接从转换点中计算出矩形的长度和宽度。也可以通过计算每个对象的凸包来计算矩形的长度和宽度。
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处理重叠矩形：如果矩形存在重叠现象，我们需要进一步处理。我们可以通过计算重叠矩形之间的交集和并集来确定矩形的最终尺寸和位置。
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示例代码：以下是一段示例代码，演示了如何从矩阵中提取和测量矩形：
def extract_rectangles(matrix):
"""Extracts rectangles from a matrix.
Args:
matrix: The input matrix.
Returns:
A list of rectangles.
"""
# Create a list to store the rectangles.
rectangles = []
# Iterate over the rows and columns of the matrix.
for i in range(matrix.shape[0]):
for j in range(matrix.shape[1]):
# If the current pixel is 1, start a new rectangle.
if matrix[i, j] == 1:
# Create a new rectangle object.
rectangle = {'x1': j, 'y1': i, 'x2': j, 'y2': i}
# Keep track of the current rectangle.
current_rectangle = rectangle
# Iterate over the remaining rows and columns of the matrix.
for k in range(i + 1, matrix.shape[0]):
for l in range(j + 1, matrix.shape[1]):
# If the current pixel is 1, update the current rectangle.
if matrix[k, l] == 1:
current_rectangle['x2'] = l
current_rectangle['y2'] = k
# Add the current rectangle to the list of rectangles.
rectangles.append(current_rectangle)
return rectangles
def measure_rectangles(rectangles):
"""Measures the width and height of a list of rectangles.
Args:
rectangles: The list of rectangles to measure.
Returns:
A list of tuples containing the width and height of each rectangle.
"""
# Create a list to store the measurements.
measurements = []
# Iterate over the list of rectangles.
for rectangle in rectangles:
# Calculate the width and height of the rectangle.
width = rectangle['x2'] - rectangle['x1'] + 1
height = rectangle['y2'] - rectangle['y1'] + 1
# Add the width and height to the list of measurements.
measurements.append((width, height))
return measurements
# Example usage.
matrix = np.array([[0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 1, 1, 1, 1, 1, 1, 1, 0, 0],
[0, 1, 1, 1, 1, 1, 1, 1, 0, 0],
[0, 1, 1, 1, 1, 1, 1, 1, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 1, 1, 1, 1, 1, 0],
[0, 0, 0, 0, 1, 1, 1, 1, 1, 0],
[0, 0, 0, 0, 0, 0, 1, 1, 0, 0]])
rectangles = extract_rectangles(matrix)
measurements = measure_rectangles(rectangles)
print("Rectangles:")
for rectangle, measurement in zip(rectangles, measurements):
print("Rectangle: ({}, {}) - ({}, {})".format(rectangle['x1'], rectangle['y1'],
rectangle['x2'], rectangle['y2']))
print("Width: {}, Height: {}".format(*measurement))
