无原图信息的网格分割乱序图像拼接算法优化求助

我花了一周开发了一款应用，目标是将被分割为x行y列并打乱的图像还原到原始状态，且无原图信息可用。查资料后发现，现有方案大多针对带边缘形状的拼图，而非这类规则网格分割的图像。

最初我尝试用遗传算法解决，但适配的适应度函数效果很差，导致耗时不稳定、还原结果不一致，于是改用基于边缘检测的适应度匹配方案：通过计算图像块边缘的匹配度来拼接还原图像，但当前算法成功率仅约20%。

核心代码（获取初始适应度值） #

def get_piece_fitness(self):  # checks how likely each piece is to be next to each other

        for piece_one in self.image_pieces:
            Helper.get_certain_loading(current_progress=piece_one.index + 1, final_num=len(self.image_pieces),
                                       description="Getting fitness values of piece edges: ")
            right_edge_fit_likelihood = []
            left_edge_fit_likelihood = []
            top_edge_fit_likelihood = []
            bottom_edge_fit_likelihood = []
            for piece_two in self.image_pieces:
                if piece_two != piece_one:  # check whether the pieces aren't the same piece

                    # concatenating horizontally on both sides at once to save on computing power
                    horizontal_edge_fit = np.concatenate(
                        [piece_two.gray_piece, piece_one.gray_piece, piece_two.gray_piece], axis=1)
                    horizontal_edge_likelihood = self.get_edge_fitness(horizontal_edge_fit, is_horizontal=True)

                    left_edge_fit_likelihood.append((piece_two, horizontal_edge_likelihood[0]))

                    right_edge_fit_likelihood.append((piece_two, horizontal_edge_likelihood[1]))

                    vertical_edge_fit = np.concatenate(
                        [piece_two.gray_piece, piece_one.gray_piece, piece_two.gray_piece])
                    vertical_edge_likelihood = self.get_edge_fitness(vertical_edge_fit, is_horizontal=False)

                    top_edge_fit_likelihood.append((piece_two, vertical_edge_likelihood[0]))

                    bottom_edge_fit_likelihood.append((piece_two, vertical_edge_likelihood[1]))

            piece_one.left_edge_candidates = left_edge_fit_likelihood
            piece_one.right_edge_candidates = right_edge_fit_likelihood
            piece_one.bottom_edge_candidates = bottom_edge_fit_likelihood
            piece_one.top_edge_candidates = top_edge_fit_likelihood

    def get_edge_fitness(self, image: np.ndarray, is_horizontal: bool) -> tuple[float, float]:
        image_blur = cv.GaussianBlur(image, (5, 5), 0)  # image blur
        edges = cv.Canny(image=image_blur, threshold1=30, threshold2=self.contrast)  # Canny Edge Detection

        if is_horizontal:
            edges_width = edges.shape[1]
            left_edge = np.array(edges[:, (edges_width // 3) - 1: (edges_width // 3)])
            right_edge = np.array(edges[:, (edges_width // 3) * 2 - 1: (edges_width // 3) * 2])

            left_edge_length = left_edge.size
            right_edge_length = right_edge.size

            left_edge_likelihood = np.sum(left_edge) / left_edge_length
            right_edge_likelihood = np.sum(right_edge) / right_edge_length

            return left_edge_likelihood, right_edge_likelihood
        else:
            edges_height = edges.shape[0]
            top_edge = np.array(edges[(edges_height // 3) - 1:(edges_height // 3)])
            bottom_edge = np.array(edges[(edges_height // 3) * 2 - 1:(edges_height // 3) * 2])

            top_edge_length = top_edge.size
            bottom_edge_length = bottom_edge.size

            top_edge_likelihood = np.sum(top_edge) / top_edge_length
            bottom_edge_likelihood = np.sum(bottom_edge) / bottom_edge_length

            return top_edge_likelihood, bottom_edge_likelihood

补充说明 #

应用可接收拼图图像的行列数等参数，当前代码已完成图像块的正确提取，仅需优化拼接算法。现寻求可行的算法改进思路或新的解决方案。

内容的提问来源于stack exchange，提问作者M3mber