The fractal geometries are applied extensively in many applications like pattern recognition, texture analysis and segmentation. The application of fractal geometry requires estimation of the fractal features. The fractal dimension and fractal length are found effective to analyze and measure image features, such as texture, resolution, etc. This paper proposes a new wavelet–fractal technique for image resolution enhancement. The resolution of the wavelet sub-bands are improved using scaling operator and then it is transformed into texture vector. The proposed method then computes fractal dimension and fractal length in gradient domain which is used for resolution enhancement. It is observed that by using scaling operator in the gradient domain, the fractal dimension and fractal length becomes scale invariant. The major advantage of the proposed wavelet–fractal technique is that the feature vector retains fractal dimension and fractal length both. Thus, the resolution enhanced image restores the texture information well. The texture information has also been observed in terms of fractal dimension with varied sample size. We present qualitative and quantitative analysis of the proposed method with existing state of art methods.

分形几何学在模式识别、纹理分析和分割等许多应用中得到广泛应用。分形几何的应用需要对分形特征进行估计。分形维数和分形长度被发现可以有效地分析和测量图像特征，如纹理、分辨率等。本文提出了一种新的用于图像分辨率增强的小波-分形技术。使用缩放算子提高小波子带的分辨率，然后将其转换为纹理向量。然后，所提出的方法计算用于分辨率增强的梯度域中的分形维数和分形长度。可以看出，通过在梯度域中使用缩放算子，分形维数和分形长度变为尺度不变。所提出的小波-分形技术的主要优点是特征向量同时保留了分形维数和分形长度。因此，分辨率增强图像很好地还原了纹理信息。在不同样本大小的分形维数方面也观察到了纹理信息。我们使用现有的最先进方法对所提出的方法进行定性和定量分析。