Is stating 'It is incumbent upon me to walk to the House of Allah' a binding vow?

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Stating, 'It is incumbent upon me to walk to the House of Allah' (Alayya al-mashyu ila Bayt Allah) constitutes a binding vow. This is supported by the report from Ibn Umar concerning a man who said this, stating it was a vow and that he must perform the walk. Similar opinions are held by Al-Qasim ibn Muhammad, Yazid ibn Ibrahim Al-Taymi, Malik, and a group of scholars. The basis for this ruling is that the word 'incumbent upon me' ('alayya) signifies self-obligation, thus making the action binding just as if he had said, 'It is incumbent upon me, a vow.'